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Product rule | Taking derivatives | Differential Calculus | Khan Academy
 
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Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/quotient-rule?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Missed the previous lesson? https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/product-rule-proof?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Calculus channel: https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 664368 Khan Academy
Product rule proof | Taking derivatives | Differential Calculus | Khan Academy
 
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Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/product-rule?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Missed the previous lesson? https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/using-the-product-rule-and-the-chain-rule?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Calculus channel: https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 93154 Khan Academy
Basic Product Rule Example #1
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Please consider supporting PJMT on Patreon! https://www.patreon.com/patrickjmt?ty=c Basic Product Rule Example #1
Views: 15890 patrickJMT
Proof of the Product Rule from Calculus
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Proof of the Product Rule from Calculus. Here I show how to prove the product rule from calculus! This is one of the reason's why we must know and use the limit definition of the derivative. After all, that IS what a derivative is... if that makes sense! :)
Views: 58200 patrickJMT
Product Rule for Derivatives  (Calculus)
 
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The product rule is one of the fundamental derivative rules in calculus. It shows you how to take the derivative of the product of two functions: f·g. In this video we will introduce the product rule, talk about common mistakes, and give several examples. ************** If you would like to help us make new videos, you can support us through Patreon at https://www.patreon.com/socratica We also welcome Bitcoin donations! Our Bitcoin address is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you!! ************** Written and Produced by Michael Harrison Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica. You can follow Michael on Twitter @mlh496 ************** You can also follow Socratica on: - Twitter: @socratica - Instagram: @SocraticaStudios - Facebook: @SocraticaStudios Please Subscribe so you'll hear about our newest videos! If you found this video helpful, please give it a "thumbs up" and share it with your friends!
Views: 30041 Socratica
The Product Rule
 
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http://mathispower4u.wordpress.com/
Views: 3275 Mathispower4u
Product Rule
 
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Product rule, step by step, derivative example. For more free calculus videos visit http://MathMeeting.com.
Views: 58927 Math Meeting
Product Rule 3
 
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Another product rule, step by step, derivative example. For more free calculus videos visit http://MathMeeting.com.
Views: 16353 Math Meeting
Derivatives... How? (NancyPi)
 
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MIT grad shows how to find derivatives using the rules (Power Rule, Product Rule, Quotient Rule, etc.). To skip ahead: 1) For how and when to use the POWER RULE, constant multiple rule, constant rule, and sum and difference rule, skip to time 0:22. 2) For the PRODUCT RULE, skip to 7:36. 3) For the QUOTIENT RULE, skip to 10:53. For my video on the CHAIN RULE for finding derivatives: https://youtu.be/H-ybCx8gt-8 For my video on the DEFINITION of the derivative: https://youtu.be/-ktrtzYVk_I Nancy formerly of MathBFF explains the steps. For more of the QUOTIENT RULE and a shortcut to remember the formula, jump to my video at: https://youtu.be/jwuiVb84Xx4 For Follow Nancy on Instagram: https://instagram.com/nancypi Twitter: https://twitter.com/nancypi What is the derivative? It's a function that gives you the instantaneous rate of change at each point of another function. You can calculate the derivative with the definition of the derivative (using the limit), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule: 1) POWER RULE: If the given equation is a polynomial, or just a power of x, then you can use the Power Rule. For a term that's just a power of x, such as x^4, you can get the derivative by bringing down the power to the front of the term as a coefficient and decreasing the x power by 1. For example, for x^4, the derivative is 4x^3. If you have many terms added or subtracted together, and if they are powers of x, you can use the Power Rule on each term (by the Sum and Difference Rules). NOTE: The derivative of a constant, just a number, is always 0 (that is the Constant Rule). Also, if you have a term that is a constant multiplied in the front of the term, like 2x^3, you can keep the constant and differentiate the rest of the term. In this example, you keep the 2 and take the derivative of x^3, which is 3x^2, so the derivative of the term 2x^3 is 2*3x^2, or 6x^2. ANOTHER NOTE:You can use the same power rule method for fractional or negative powers, but be careful... for negative powers, it works as long as x is not 0, and for fractional/rational powers, if the power is less than 1, your derivative won't be defined at x = 0. 2) PRODUCT RULE: If your equation is not a polynomial but instead has the overall form of one expression multiplied by another expression, then you can use the Product Rule. The Product Rule says that the derivative of two functions multiplied together is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. 3) QUOTIENT RULE: If your equation has the overall form of one expression divided by another expression, then you can use the Quotient Rule. The Quotient Rule says that the derivative of one function divided by another (a quotient) is equal to the bottom function times the derivative of the top bottom minus the top function times the derivative of the bottom function, all divided by the bottom function squared. This is true as long as the bottom function is not equal to 0. For more of my math videos, check out: http://nancypi.com
Views: 148630 NancyPi
03 - Product Rule of Differentiation in Calculus, Part 1
 
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Get more lessons & courses at http://www.MathTutorDVD.com. Learn how to use the product rule to take the derivative of a function in calculus 1.
Views: 612 mathtutordvd
Product Rule for Exponents
 
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This is the product rule for exponents. The derivation and several examples are presented for multiplying terms with the same base.
Views: 27455 Mathbyfives
Product rule - Calculus derivatives tutorial
 
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Learn how to take the derivative of a function using the product rule. This complete calculus derivatives tutorial explains why and how to use the product rule. To see all my calculus videos check out my website http://MathMeeting.com My name is Chris and my passion is to teach math. Learning should never be a struggle which is why I make all my videos as simple and fun as possible. I cover all subjects from basic level math through upper level calculus and statistics. I also make brain teaser, word problems, and Rubik's cube videos for fun. Website - http://MathMeeting.com Channel Page - http://Youtube.com/MathMeeting Facebook Page - http://facebook.com/MathMeeting Patreon Page - http://patreon.com/MathMeeting
Views: 2249 Math Meeting
Power Rule, Product & Quotient Rule - Exponents, Fractions, Square Roots - Derivatives & Calculus
 
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This calculus video tutorial explains how to find the derivative using the power rule, product rule, and quotient rule. It contain examples of using the power rule on exponents, fractions, and square root functions. It contains plenty of practice problems for you to work on.
A Derivative Using the Product Rule - Calculus
 
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An example of applying the product rule to differentiate a function with two factors.
Views: 1504 Mr. S Math
How To Use The Product Rule - VCE Maths Methods
 
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http://www.BetterMarksInMaths.com/vce-maths-methods-tutorials This lesson will show you how to Differentiate the product of a Square Root function and a Quadratic function using the product rule. Get help with the questions you're stuck on in the Free members area for VCE Maths Methods Unit 3 & 4.
Views: 3931 BetterMarksInMaths
Ex: Find a Derivative Using Product Rule (Basic Example)
 
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This video explains how to apply the product rule of differentiation to find the derivative of a function that is given as a product of two quadratic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
Views: 10210 Mathispower4u
Derivatives - Power, Product, Quotient and Chain Rule - Functions & Radicals - Calculus Review
 
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This calculus video tutorial shows you how to find the derivative of any function using the power rule, quotient rule, chain rule, and product rule. It shows you how to differentiate polynomial, rational functions, trigonometric functions, inverse functions, exponential equations and logarithmic functions. It's a nice review of calculus in preparation for your next test or exam. Understand Calculus In 35 Minutes: https://www.youtube.com/watch?v=WsQQvHm4lSw Basic Integration Rules: https://www.youtube.com/watch?v=WDZMjYJyH6k Intro To Chemistry: https://www.youtube.com/watch?v=-KfG8kH-r3Y Intro To Physics: https://www.youtube.com/watch?v=WL5_T-g3Fxw Epic Music Mix: https://www.youtube.com/watch?v=qeljbZhx9bY Excel Tutorial For Beginners: https://www.youtube.com/watch?v=nK-uNYuvcag How To Receive Tutoring and Get Paid At The Same Time: https://www.youtube.com/watch?v=J8A8JTpOWCQ How To Lose Weight Fast! https://www.youtube.com/watch?v=cC4FUSZunsY Here's a list of topics covered in this review of derivatives: 1. How To Find The Derivative of a Constant 2. How To Calculate The Derivative Using The Power Rule on a Monomial or Polynomial 3. Derivative of Fractions and Negative Exponents 4. Derivative of Radicals and Fractional Exponents 5. Derivative of Trigonometric Functions - Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant 6. Derivative of Natural Logarithms / Logs 7. Derivatives of Logarithms 8. Derivatives of Exponential Functions - e^x or a^x 9. Logarithmic Differentiation 10. Product Rule, Quotient Rule, and Chain Rule 11. Implicit Differentiation 12. How To Differentiate With Respect to Another Variable Such as y or time for related rate problems 13. How To Find The Derivative of an Inverse Function 14. How To Find The Derivative Using Limits - Radicals, Fractions, Exponents & Factoring Here's a list of problems covered in this video: 1. 5, 8, pi, pi^e, 4e 2. x^2, x^3, x^4, x^5 3. 4x^5, 7x^6, 8x^3 4. 4x^3 + 8x^2 - 7x + 6 5. 5x, 8x, 12x, x^1 6. 1/x^2, 1/x^3, 1/x^5, 7/x^6 7. sqrt(x), cube root(x^4), x^(3/7) 8. 8x^5 - 3/x^3 + x^(4/5) 9. sin(x), cos(x^3), tan(x^4), sec(7x), cot(x^4), csc(x^3+x^2) 10. ln(x), ln(x^2), ln(x^4-x^3), ln(sinx) 11. log5(x^3+x^2), log4(x^3) 12. e^x, e^2x, e^3x, e^x^2, e^tanx 13. 5^x, 7^x^2, 8^x^3, x^3, 3^x, x^x, x^sinx 14. (x^2)(sinx), x^3ex^2, x^4lnx 15. (x^3+6x)/(5x-8), (x^3+7x^2)/12x^5, sin(x^4), (x^3+5x^2)^4 16. tan(sinx^4), sin^3(cos(tanx^5)) 17. x^3+y^3=8, x^2+2xy+y^2=7, tan(xy)=7
Differentiation - Product Rule with Easy Exampls  | Stay Learning |CBSE (HINDI | हिंदी)
 
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Topics Covered in this Video - Product Rule - Examples To View Full Video Lectures Visit - https://bit.ly/2PEEnUC ★ ACCOUNTS VIDEOS ★ https://www.youtube.com/channel/UCAXbiqmSkp9Sse4guGRMqDw?view_as=subscriber ★ COST ACCOUNTING VIDEOS ★ https://www.youtube.com/channel/UCAXbiqmSkp9Sse4guGRMqDw?view_as=subscriber ★ FINANCIAL MANAGEMENT VIDEOS ★ https://www.youtube.com/channel/UCAXbiqmSkp9Sse4guGRMqDw?view_as=subscriber ★ ECONOMICS VIDEOS ★ https://www.youtube.com/channel/UCK5RB8xNW_iOXz-rcGJZyTw?view_as=subscriber ★ INCOME TAX VIDEOS ★ https://www.youtube.com/channel/UCRRFVa1axTUdwZzc4Ta42XQ?view_as=subscriber ★ MATHS VIDEOS ★ https://www.youtube.com/channel/UCaIY3jMl7QDUWN6P6kSUYWw?view_as=subscriber STUDY TIPS ऐसे पढोगे तो हमेशा TOPPER बनोगे | Study Tips https://bit.ly/2QUXaew ENGLISH – Fatafat (Easy Way to Learn English) अंग्रेजी सीखें - फटाफट https://bit.ly/2PoAF4H ★ ExpertMotivation Channel https://bit.ly/2EsPBKC ★ For Any Information Video classes & Face To Face Batches Call +91 9268373738 E-mail: [email protected] (We Prefer emails rather than calls) Call timings Monday to Friday - Morning 10 to Evening 7 FACEBOOK: https://www.facebook.com/VijayAdarshIndia WEBSITE: http://www.vijayadarsh.com
Views: 105401 StayLearning
Derivatives - Product + Chain Rule + Factoring
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Derivatives - Product + Chain Rule + Factoring - A quick example for a friend out there in internet land! For more free math videos, check out http://PatrickJMT.com
Views: 395398 patrickJMT
Product Rule to Find a Derivative : Basic Example , No Simplifying
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Product Rule to Find a Derivative : Basic Example , No Simplifying
Views: 14936 patrickJMT
The Chain Rule... How? When? (NancyPi)
 
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MIT grad shows how to use the chain rule to find the derivative and WHEN to use it. To skip ahead: 1) For how to use the CHAIN RULE or "OUTSIDE-INSIDE rule", skip to time 0:17. 1b) For how to know WHEN YOU NEED the chain rule, skip to 4:35. 2) For another example with the POWER RULE in the chain rule, skip to 7:05. 3) For a TRIG derivative chain rule example, skip to 9:33. 3b) For the formal chain rule FORMULA, skip to 11:36. PS) For a DOUBLE CHAIN RULE (or "repeated use of the chain rule") example, skip to 13:33. Nancy formerly of MathBFF explains the steps. Follow Nancy on Instagram: https://instagram.com/nancypi Twitter: https://twitter.com/nancypi 1) The CHAIN RULE is one of the derivative rules. You need it to take the derivative when you have a function inside a function, or a "composite function". For ex, in the equation y = (3x + 1)^7, since the function 3x+1 is inside a larger, outer function, the power of 7, you'll need the chain rule to find the correct derivative. How do you use the chain rule? You can think of it as the "OUTSIDE-INSIDE" rule: take the DERIVATIVE of JUST the OUTSIDE function first, LEAVING THE INSIDE FUNCTION alone (unchanged), then MULTIPLY BY the DERIVATIVE of JUST the INSIDE function. Sometimes you might hear this expressed as: take the derivative of the outer function, "evaluated at the inner function", times the derivative of just the inner function. For our ex, first take the derivative of the outer function (the power of 7) to get 7*(3x + 1)^6 since the derivative "power rule" tells you to bring down the power to the front (as a constant or coefficient just multiplied in the front) and then decrease the power by 1, which leaves a power of 6. Notice that you leave the inside function the way it is and just rewrite it for now. Then you multiply by the derivative of just the inner function, 3x + 1. Since the derivative of 3x + 1 is just 3, the full derivative (dy/dx) is: 7*[(3x + 1)^6]*3, which is just 21(3x + 1)^6. 1b) HOW do you know WHEN TO USE the chain rule? If the original equation had just been x^7, there would be no need for the chain rule. It's when you have something more than just x inside that you should use the chain rule, such as (3x + 1)^7 or even (x^2 + 1)^7. Sometimes the chain rule may make no difference. For instance, if you have the function (x + 1)^7, taking the derivative of the inside function just gives you 1, so multiplying by that inside derivative of 1 will not change the overall answer. However, it can't hurt to use the chain rule anyway, so it's a good idea to get in the habit of using it so that you don't forget it when it really does make a difference. 2) Another chain POWER RULE example: To find the derivative of h(x) = (x^2 + 5x - 6)^9, use the same steps as above to first take the outside derivative and then multiply by the inside derivative. In this case, the derivative, dh/dx (or h'(x)) is equal to 9(x^2 + 5x - 6)^8 * (2x + 5). Using the chain rule with the power rule is sometimes called the "power chain rule". 3) TRIG EXAMPLE: the idea is the same as above even if you're using the chain rule to differentiate something like a trigonometric function. If you have anything more than just x inside the trig function, you'll need the chain rule to find the derivative. For the equation y = sin(x^2 - 3x), you first take the derivative of the outer function, just the sine function. Since the derivative of sine is cosine, the outside derivative (with the inside left unchanged) is cos(x^2 - 3x). Then, find the derivative of just the inside (of just the x^2 - 3x part), and multiply by that. Since the derivative of x^2 - 3x is 2x - 3, the full derivative answer is dy/dx = cos(x^2 - 3x)*(2x - 3). 3b) FORMULA: Although it's easier to think about the chain rule as the "outside-inside rule", if for any reason you have to use the formal chain rule formula, check out the two versions I show here. Both are based on the equation being a composition of functions, f(g(x)). The second version shown uses Liebniz notation. Either way, both show a component of the derivative that comes from the inside function, and it's important not to forget to multiply by this inside derivative factor if you want to get the right full derivative answer. P.S.) DOUBLE CHAIN RULE: Sometimes you might have to use the chain rule more than once, known as "repeated use of the chain rule". In y = (1 + cos2x)^2, not only would you need to take the derivative of the outside power of 2, as well as multiply by the derivative of the inside function, 1 + cos2x, but after that you would ALSO then need to multiply by the derivative of the 2x inside cosine because that inside function was 1 + cos2x and not just 1 + cosx. This means you would use the chain rule twice. The idea is that you have to keep taking the derivative of the inner functions until you have reached every inner function that is more complicated than just "x". For more calculus math videos, check out: http://nancypi.com
Views: 188941 NancyPi
Math for fun#8, FAKE PRODUCT RULE
 
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Math for fun#8, FAKE PRODUCT RULE, more math for fun: https://www.youtube.com/playlist?list=PLj7p5OoL6vGxe7hIWOKfevOet0e1jOezd derivative product rule, find f and g so that the derivative of a product is the product of the derivative, math fun facts about derivative, calculus product rule, calculus derivative, hard derivative problem, hard math problem, challenging math problems, hard algebra problems, hard calculus problems, blackpenredpen follow me: https://twitter.com/blackpenredpen
Views: 27484 blackpenredpen
Quotient rule from product & chain rules | Derivative rules | AP Calculus AB | Khan Academy
 
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Sal shows how you can derive the quotient rule using the product rule and the chain rule (one less rule to memorize!). Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-diff-mul-rules/v/differentiating-using-multiple-rules-strategy?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-derivtive-rules-opt-vids/v/chain-rule-proof?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 272310 Khan Academy
Proof:  The Product Rule of Differentiation
 
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This video explains the proof of the product rule using the limit definition of the derivative. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
Views: 8567 Mathispower4u
Derivatives of Trigonometric Functions - Product Rule Quotient & Chain Rule - Calculus Tutorial
 
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This calculus video tutorial explains how to find the derivative of trigonometric functions such as sinx, cosx, tanx, secx, cscx, and cotx. It contain examples and practice problems involving the use of the product rule, quotient rule, and chain rule. Here is a list of topics: 1. Derivative of the six trigonometric functions - sin, cos, tan, cot, sec, and csc 2. Derivative of Polynomial Functions with Trig Functions 3. Product Rule - Derivative of x^2 sinx and x^3 cosx 4. Quotient Rule - Derivative of Fractions and Rational Functions 5. Chain Rule - Derivative of Composite functions 6. Derivative of sin(5x), cos(x^3), sec(x^2), tan(sin4x), sin^2(3x) 7. Trig functions inside of other trigonometric functions 8. prove d/dx (secx) = secxtanx 9. prove d/dx (cotx) = -csc^2 x 10. trigonometric proofs
Product Rule for Derivatives
 
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When the Basic Differentiation Rules aren't enough... In this video I do 4 examples of finding the Derivative of a function using the Product Rule. The textbook I teach from states the product rule as d/dx[f(x)g(x)]=f(x)g'(x)+-g(x)f'(x) instead of d/dx(f(x)g(x))=f(x)g'(x)+-f'(x­)g(x) and I have adjusted my class notes to reflect this discrepancy. I have checked all of the examples in this video and the final answers are correct. Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
Views: 31148 ProfRobBob
[Discrete Math 1] Rule of Sum and Rule of Product Examples
 
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LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Submit your questions on Reddit: http://bit.ly/1GwZZrP We do some problems related to the rule of product and rule of sum. Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
Views: 33947 TheTrevTutor
Derivatives using the Product Rule
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Derivatives using the Product Rule.
Views: 17082 patrickJMT
Chain Rule For Finding Derivatives
 
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This calculus video tutorial explains how to find derivatives using the chain rule. This lesson contains plenty of practice problems including examples of chain rule problems with trig functions, square root & radicals, fractions, ln, product rule, and quotient rule. This video gives you a simple way to find the derivative of a function using the chain rule.
Quotient Rule Made Easier (NancyPi)
 
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MIT grad shows an easy way to use the Quotient Rule to differentiate rational functions and a shortcut to remember the formula. The calculus Quotient Rule derivative rule is one of the derivative rules for differentiation. It's used to take the derivative of a rational function. To skip ahead: 1) For an easy way to remember the Quotient Rule formula, skip to time 0:21. 2) For an example of how to use the Quotient Rule to take the derivative of a fraction or quotient of functions (rational function), skip to 1:41. This video is a basic introduction to the Quotient Rule for taking derivatives in calculus. Nancy formerly of MathBFF explains the steps. For more help with Quotient Rule derivatives and HOW TO TAKE THE DERIVATIVE of a function using the DERIVATIVE RULES (Power Rule, Product Rule, Quotient Rule), jump to: https://youtu.be/QqF3i1pnyzU Follow Nancy on Instagram: https://instagram.com/nancypi Twitter: https://twitter.com/nancypi The Quotient Rule (calculus) tells you how to find the derivative of rational functions (a fraction, or one function divided by another function). The formal definition (textbook definition) of the Quotient Rule is often unnecessarily complex and intimidating. There is a memory trick, or mnemonic, for how to remember the Quotient Rule formula. All you need to remember is the song "LO dee-HI minus HI dee-LO, over LO LO," where "dee" means the "derivative of." "HI" means your top function in the numerator, and "LO" means your bottom function in the denominator. In other words, multiply the bottom function times the derivative of the top function MINUS the top function times the derivative of the bottom function, then DIVIDED by the bottom function times itself. After you differentiate the function with the Quotient Rule, remember to simplify the expression as much as possible using algebra. This video is a basic intro to the Quotient Rule. For more of my calculus math videos and examples of taking derivatives, differentiation rules like the chain rule, differential calculus, basic calculus, integral calculus, common derivatives, and calculus problems (including Calculus 1, AP Calculus AB, AP Calculus BC, and Calculus 2), as well as precalculus and algebra math help, check out: http://nancypi.com
Views: 22269 NancyPi
Multivariate Calculus – Product rule
 
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Course 2 - Mathematics for Machine Learning Multivariate Calculus, Module 1 What is calculus To get certificate subscribe at: https://www.coursera.org/learn/multivariate-calculus-machine-learning ============================ Mathematics for Machine Learning: Multivariate Calculus https://www.youtube.com/playlist?list=PL2jykFOD1AWaL4_-bdidPfIWe765jOgfL ============================ Youtube channel: https://www.youtube.com/user/intrigano ============================ https://scsa.ge/en/online-courses/ https://www.facebook.com/cyberassociation/ About this course: This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you’ll still come away with the confidence to dive into some more focused machine learning courses in future. Who is this class for: This class is for people who would like to learn more about machine learning techniques, but don’t currently have the fundamental mathematics in place to go into much detail. This course will include some exercises that require you to work with code. If you've not had much experience with code before DON'T PANIC, we will give you lots of guidance as you go. Module 1 What is calculus Understanding calculus is central to understanding machine learning! You can think of calculus as simply a set of tools for analysing the relationship between functions and their inputs. Typically, in machine learning, we are trying to find the inputs which enable a function to best match the data. We start this module from the basics, by recalling what a function is and where we might encounter one. Following this, we talk about the how, when sketching a function on a graph, the slope describes the rate of change off the output with respect to an input. Using this visual intuition we next derive a robust mathematical definition of a derivative, which we then use to differentiate some interesting functions. Finally, by studying a few examples, we develop four handy time saving rules that enable us to speed up differentiation for many common scenarios. Learning Objectives • Recall the definition of differentiation • Apply differentiation to simple functions • Describe the utility of time saving rules • Apply sum, product and chain rules
Views: 341 intrigano
Derivatives of Exponential Functions
 
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This calculus video tutorial explains how to find the derivative of exponential functions using a simple formula. It explains how to do so with the natural base e or with any other number. This video contains plenty of examples and practice problems including those using the product rule and quotient rule for derivatives. Calculus Video Playlist: https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1 Access to Premium Videos: https://www.patreon.com/MathScienceTutor https://www.facebook.com/MathScienceTutoring/
Screencast 2.3.2: Product Rule examples
 
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Two quick examples of the Product Rule in action, and one example where you should NOT use the Product Rule.
Views: 3308 GVSUmath
A Derivative Using the Product Rule Involving a Radical - Calculus
 
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An example of applying the product rule to differentiate a function involving a radical, in this case a square root.
Views: 2370 Mr. S Math
Proof of Product Rule
 
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When we cover the product rule in class, it's just given and we do a LOT of practice with it. Hopefully all of you are wondering where it comes from...this is it. You just use the limit definition of the derivative and a little trick. Sometimes this is called finding the derivative from first principles.
Views: 1708 turksvids
Calculus: Quotient Rule and Simplifying
 
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Quotient Rule and Simplifying. Just a basic example of using the quotient rule and simplifying.
Views: 252582 patrickJMT
Product Rule and Quotient Rule | MIT Highlights of Calculus
 
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Product Rule and Quotient Rule Instructor: Gilbert Strang http://ocw.mit.edu/highlights-of-calculus License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu Subtitles are provided through the generous assistance of Jimmy Ren.
Views: 50576 MIT OpenCourseWare
How to Do Implicit Differentiation (NancyPi)
 
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MIT grad shows how to do implicit differentiation to find dy/dx (Calculus). To skip ahead: 1) For a BASIC example using the POWER RULE, skip to time 3:57. 2) For an example that uses a TRIG FUNCTION and the PRODUCT RULE, skip to time 7:20. Nancy formerly of MathBFF explains the steps. Follow Nancy on Instagram: https://instagram.com/nancypi Twitter: https://twitter.com/nancypi What is implicit differentiation? Up until now, most functions you've had to differentiate have probably been written EXPLICITLY as a function of x, such as y = x^2. However, if a function y is written IMPLICITLY as a function of x, such as x^2 + y^2 = 9, you will need to use implicit differentiation to find the derivative dy/dx. The only difference is that any time you take the derivative of y, you must also multiply by dy/dx. The reason is that y is dependent on x. You can think of y as containing some x expression inside it, so implicit differentiation is basically a special instance of the chain rule in which you must take the outside derivative but also multiply by the inside derivative, which is dy/dx in this case. Here are the steps to doing implicit differentiation to find DY/DX: 1) TAKE THE DERIVATIVE OF BOTH SIDES, MULTIPLYING BY DY/DX every time you take the derivative of a Y: The first step is to take the derivative of both sides of the equation, with respect to x, but to attach a dy/dx if you ever take the derivative of y. For instance, to implicitly differentiate the equation x^2 + y^2 = 9, take the derivative of both sides with respect to x. On the left, the derivative of the x^2 term is just 2x. To differentiate the y^2 term, in this case first use the power rule to get 2y, and THEN, because y is dependent on x, you must multiply the term by dy/dx so that you have y^2 times dy/dx. Don't forget to differentiate the right side of the original equation as well, which was the constant 9, so the derivative is just 0. Your new, differentiated equation is then 2x plus y^2 dy/dx = 0. 2) GET DY/DX ALONE ON ONE SIDE: The third step is to solve for dy/dx, or in other words, to get dy/dx alone on one side of the equation. Next, DISTRIBUTE AND EXPAND BOTH SIDES if necessary distributing or opening up any terms that have parentheses. Then, if dy/dx appears in more than one term, get those terms together on one side and use the SIMPLIFICATION TRICK OF FACTORING out dy/dx from those terms so that it then appears only once on that side. Finally, DIVIDE OUT any factor that is currently multiplied by the dy/dx so that you are left with dy/dx alone on one side and an equation that looks like dy/dx = some other expression. NOTE: Only multiply by dy/dx if you are taking the derivative of y. In more challenging examples like the second example in this video, you do not need to attach a dy/dx if you are just multiplying by y. For instance, when differentiating a term like xy, using the product rule gives you x times dy/dx plus y. Notice that in the second term from the product rule, it was not necessary to attach a dy/dx to the y, since you were not taking the derivative of y in that term. For more of my calculus and math videos, check out: http://nancypi.com
Views: 133901 NancyPi
Learn how to use the product rule to find the derivative
 
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Learn how to find the derivative of a function using the product rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a function is called differentiation. There are various methods of finding the derivative of a function including, direct differentiation, product rule, quotient rule, chain rule (funtion of a function), etc. When given a function of the form y = f(x)g(x), then the derivative of the function is given by y' = f'(x)g(x) + f(x)g'(x). This method of differentiation is called the produt rule. The product rule is used to find the derivative of a function that is a product of two functions.
Views: 396 Brian McLogan
Functions and Proof of Calculus Product Rule Using the Definition of a Derivative
 
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Functions and Proof of Calculus Product Rule Using the Definition of a Derivative
Views: 137 Mike Gaffney
Product Rule Differentiation, Differentiation Formulas by Shobhit Sir
 
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Product Rule Differentiation , Differentiation Formulas The product rule is a formal rule for differentiating problems where one function is multiplied by another. The rule follows from the limit definition of derivative and is given by. . Remember the rule in the following way. Each time, differentiate a different function in the product and add the two terms together. The product rule is used in calculus when you are asked to take the derivative of a function that is the multiplication of a couple or several smaller functions. In other words, a function f(x) is a product of functions if it can be written as g(x)h(x), and so on. product rule differentiation The Power of a Product rule is another way to simplify exponents. First, we need to define some terms as they relate to exponents. When you have a number or variable raised to a power, it is called the base, while the superscript number, or the number after the '^' mark, is called the exponent or power. product rule for differentiation Examples. Suppose we want to differentiate ƒ(x) = x2sin(x). By using the product rule, one gets the derivative ƒ '(x) = 2x sin(x) + x2cos(x) (since the derivative of x2 is 2x and the derivative of sin(x) is cos(x)). ... This, combined with the sum rule for derivatives, shows that differentiation is linear. visit us @ http://www.machephy.org/ like our page : https://www.facebook.com/machephy.eduworld/ follows us : https://twitter.com/Machephy_eduwor https://www.instagram.com/machephy_eduworld/ Call us @099308 79712 for more details
Views: 1285 MaChePhy Eduworld
Ex 2:  Implicit Differentiation Using the Product Rule
 
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This video explains how to determine dy/dx for the equation (x^2)(x^2) = 16 using implicit differentiation. Then it shows how to determine the equation of the tangent line at (4,-1) Complete Video Library at www.mathispower4u.com
Views: 12095 Mathispower4u
Calculus - Find the derivative of inverse trigonometric functions
 
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This video covers the derivative rules for inverse trigonometric functions like, inverse sine, inverse cosine, and inverse tangent. For the examples it will be helpful to know the product rule and chain rule for derivatives. Remember to check your math book as these rules may be slightly different depending on how the inverse functions are defined. Did you find this video helpful and want to find even more? See all of the subjects available and stay up to date with the newest videos at: http://www.MySecretMathTutor.com This video is related to many other topics. Check them out: The basic rules for derivatives: https://youtu.be/rRphiUtRKcY The power rule: https://youtu.be/pBc4Udqw330 The chain rule: https://youtu.be/Jf38DwIV6U4 The product rule: https://youtu.be/FBfXqorEad0 You can make MySecretMathTutor even better by contributing community subtitles. http://www.youtube.com/timedtext_cs_panel?c=UCcBOg_7QmpJFlIVMYDyUhaw&tab=2 Have an idea for a future video? Send me a message! http://www.mysecretmathtutor.com/contact-me.html Follow us on Facebook: https://www.facebook.com/pg/My-Secret-Math-Tutor-177258548991955/about/
Views: 50770 MySecretMathTutor
Power Rule... How? (NancyPi)
 
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MIT grad shows how to find the derivative using the Power Rule, one of the derivative rules in calculus. It is a shortcut for taking derivatives of polynomial functions with powers of x. To skip ahead: 1) For HOW and WHEN to use the power rule, skip to time 0:22. 2) For how to use the power rule when you have a FRACTIONAL or NEGATIVE POWER, skip to 5:22. For my video on the other differentiation rules, PRODUCT RULE and QUOTIENT RULE, skip to https://youtu.be/QqF3i1pnyzU?t=456 Nancy formerly of mathbff explains the steps: For how to differentiate using the formal LIMIT DEFINITION of the derivative instead, jump to https://youtu.be/-ktrtzYVk_I?t=628 Support Nancy on Patreon: https://www.patreon.com/nancypi Follow Nancy on Instagram: https://instagram.com/nancypi Follow Nancy on Twitter: https://twitter.com/nancypi HOW and WHEN to use the POWER RULE: If the given equation is a polynomial, or just a power of x, then you can use the Power Rule. For a term that's just a power of x, such as x^4, you can get the derivative by bringing down the power to the front of the term as a coefficient and decreasing the x power by 1. For example, for x^4, the derivative is 4x^3. If you have many terms added or subtracted together, and if they are powers of x, you can use the Power Rule on each term (by the Sum and Difference Rules). NOTE: The derivative of a constant, just a number, is always 0 (that is the Constant Rule). Also, if you have a term that is a constant multiplied in the front of the term, like 2x^3, you can keep the constant and differentiate the rest of the term (Constant Multiple Rule). In this example, you keep the 2 and take the derivative of x^3, which is 3x^2, so the derivative of the term 2x^3 is 2*3x^2, or 6x^2. ANOTHER NOTE: You can use the same power rule method for fractional or negative powers, but be careful... for negative powers, it works as long as x is not 0, and for fractional/rational powers, if the power is less than 1, your derivative won't be defined at x = 0. The derivative is a function that gives you the instantaneous rate of change at each point of another function. You can calculate the derivative with the definition of the derivative (using the limit, see https://youtu.be/-ktrtzYVk_I?t=628), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule. For my video on the CHAIN RULE for finding derivatives, jump to https://youtu.be/H-ybCx8gt-8 For more math help and videos, check out: http://nancypi.com Editor: Miriam Nielsen of zentouro https://www.youtube.com/zentouro Director: Kristopher Knight https://kristopherknight.com
Views: 26043 NancyPi
Partial Derivatives - Multivariable Calculus
 
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This calculus 3 video tutorial explains how to find first order partial derivatives of functions with two and three variables. It provides examples of differentiating functions with respect to x or with respect to y using techniques such as the product rule, quotient rule, and power rule. This video contains plenty of examples and practice problems. Here is a list of topics: 1. Partial Derivatives - Basic Introduction 2. First Order Partial Derivatives 3. Differentiating Exponential Functions 4. Partial Differentiation of Polynomial Functions 5. Partial Derivatives of Natural Logarithmic Functions 6. First Order Partial Derivatives of Trigonometric Functions 7. Product Rule and Quotient Rule With Partial Derivatives 8. Evaluating Partial Derivatives of Functions at a Point 9. Finding The Slope of the Surface in the x direction and in the y direction 10. Higher Order Partial Derivatives - Examples and Practice Problems 11. Second Order Partial Derivatives - All Four, fxx, fxy, fyx, fyy 12. dz/dx vs dz/dy 13. Third Order Partial Derivatives - fxyz, fyyx, fyxy, fxyy 14. Equality of Mixed Partial Derivatives 15. Partial Derivatives of a function of two variables 16. Partial Derivatives 3 Variables
The Product Rule -- Derivatives -- ThatTutorGuy.com
 
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Calculus got you down? For Chris's videos covering the rest of calculus check out http://www.ThatTutorGuy.com
Views: 27139 ThatTutorGuy
Calculus Derivative Rules & How To Remember Them
 
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Know Product, Quotient and Chain rules" for taking the derivatives in 12 minutes! And I will also show you 4 derivative examples. Enjoy! So you think you can take the derivative (Product Rule, Quotient Rule, Chain Rule), handout here: https://blackpenredpen.com/calc1 Please subscribe and share my videos to help my channel grow! 😃 Comment #YAY down below & your comment might be featured in my future videos!!! My simple setup: 😃 https://youtu.be/IKk7k-CMttE , Check out my site & social media 😃 www.blackpenredpen.com 😃 [email protected] 😃 https://twitter.com/blackpenredpen 😃 https://www.instagram.com/blackpenredpen/ Thank you for watching! blackpenredpen | 曹老師 #SoYouThinkYouCantTakeTheDerivatives #CalculusLesson
Views: 3702 blackpenredpen
Ex:  Find the Equation of a Tangent Line Using the Product Rule
 
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This video provides and example of how to determine the equation of a tangent line to a function using the product rule. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
Views: 6222 Mathispower4u
Product rule from first principles
 
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This video shows how the product rule of differentiation follows from the definition of a derivative. It is shown how the rule is immediately applicable to products of three or more functions and an example is calculated.
Ex: Find a Derivative Function and Derivative Value Using the Product Rule (3 products)
 
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This video explains how to find the derivative of f(x)=x*cos(x)*sin(x) and then determine the derivative function value at 2 x-values. Site: http://mathispower4u.com
Views: 9914 Mathispower4u

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