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Basic Product Rule Example #1

Views: 16671
patrickJMT

This calculus video tutorial provides a basic introduction into the product rule for derivatives. It explains how to find the derivative of a function that contains two factors multiplied to each other. It also explains how to use the product rule to find the derivative of a function with 3 factors. This video contains plenty of examples and practice problems.
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Views: 27991
The Organic Chemistry Tutor

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

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blackpenredpen

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.
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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

Views: 587611
The Organic Chemistry Tutor

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.
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Views: 676461
Khan Academy

In this video I will explain a product rule calculus problem.
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So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Views: 9064
Krista King

The "product rule " for exponents states that when multiplying two powers you can add the exponents of like bases.
For example, 2x cubed times 4x cubed would equal 8x to the fourth
Again, multiply the numbers and add the exponents of the bases that are the same.

Views: 121
MooMoo Math and Science

This calculus video tutorial explains the concept of implicit differentiation and how to use it to differentiate trig functions using the product rule, quotient rule - fractions, and chain rule. Examples and practice problems Include Implicit differentiation with first and second derivatives and radical / square root functions.

Views: 173901
The Organic Chemistry Tutor

Visit http://ilectureonline.com for more math and science lectures!
This video is part of an eight 8 part lecture series on derivatives. Different algebraic expressions require different techniques in order to discover their derivation. I encourage you to watch the whole series and familiarize yourself with each technique as calculus is the key to understanding pretty much everything about the world!

Views: 71631
Michel van Biezen

How to use the product rule and chain rule together in solving this problem

Views: 2413
That English Mathematician

LEARN UV RULE DIFFERENTIATION WITH EXAMPLES
LEARN HOW TO FIND DERIVATIVE USING UV RULE
LEARN HOW TO USE UV RULE IN DIFFERENTIATION
PRACTICE PROBLEMS OF UV RULE
PRODUCT RULE AND QUOTIENT RULE USING DIFFERENTIATION
UV RULE | PRODUCT RULE | DERIVATIVE USING UV RULE | NCERT CLASS 12 DERIVATIVES

Views: 2873
BRMATHSCLASS

In this video I go over a useful word problem on using the product rule for derivatives in estimating the amount of phone lines a phone company needs to install in the next month.
Download the notes in my video: https://www.dropbox.com/s/71qsx78kdnn9v0y/386%20-%20Product%20Rule%20for%20Derivatives%20-%20Example%20Word%20Problem.pdf
Related Videos:
Derivative Rules - Proof of the Product Rule: http://youtu.be/EIjvGJhDAOk
Product Rule for Derivatives: Examples: http://youtu.be/_2E6UVb2d7g
Product Rule for Derivatives: Example - Simplifying Functions: http://youtu.be/l7DUz001fzg .
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Views: 2587
Math Easy Solutions

You've seen derivatives done in class, but once you try to do them on your own, you're stuck! Then you're in the right place! In this video we carefully work through derivative problems using the product, quotient and chain rule. We start with simple problems, all the way up to complicated, multi-page problems. See how all of this can be made simple!

Views: 114
Simple Math

For more free math help visit www.TheVirtual Mathematician.com
Please feel free to leave any questions in the comments.
This video will explain the concept of how to take derivatives using the product rule, as well as two example problems, in under 3 minutes. The product rule is something we want to use in calculus whenever we are attempting to take the derivative of two functions that are multiplied together. This concept will show up again and again, so let this video show you how to handle these types of problems.

Views: 3317
The Virtual Mathematician

Continue learning the quotient rule by watching this harder derivative tutorial. To see all my videos on the quotient rule check out my website at 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: 20653
Math Meeting

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.

Views: 276989
The Organic Chemistry Tutor

product rule and quotient rule for derivative in one problem,
derivative of x*e^x/(1+e^x)
So You Think You Can Take The Derivatives, file: https://blackpenredpen.com/calc1
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#Derivatives
Thank you for watching, be sure to subscribe for more new math contents!
blackpenredpen | 曹老師

Views: 3896
blackpenredpen

Learn the product rule of differentiation via example. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/primer_dif.html

Views: 20083
numericalmethodsguy

Free Calculus lecture presented by http://www.free-academy.com. This lecture practices solving derivatives using the product rule.

Views: 312
FreeAcademy

This is one of a series of video on genetics. This video will provide some complete dominance Punnett square practice problems involving the product rule. Sometimes you might be interested in finding out the probability of two traits being passed on together. The product rule is a simple way to do just that.

Views: 3042
BiologyMonk

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: 260790
patrickJMT

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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: 36343
TheTrevTutor

Donate here: http://www.aklectures.com/donate.php
Website video link: http://www.aklectures.com/lecture/sum-and-product-rule-in-genetics
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Views: 25184
AK LECTURES

Simple monohybrid, product rule, sum rule, conditional probability.

Views: 21979
Cheryl Van Buskirk

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

Views: 283011
The Organic Chemistry Tutor

In Calculus, Product rule formula is used when you have to find the derivatives of products of two or more function. When three functions in multiplication, and we have to find it's derivative, then we can find it's derivative one by one.
For example :
F(x) = u •v•w
And we have to find it's derivative
Then, f'(x) =( v•w•u') + (u•w•v') + (u•v•w')
Also, know when to use product rule vs chain rule, we tried to cover product rule problems with simple product rule formula (calculus).

Views: 535
Skill Ark

In this video we go over an example problem that has us dealing with using the product rule to predict the probability of getting certain genotypes and phenotypes in offspring from a parental cross.
If you like this video consider subscribing to improve video quality.

Views: 6134
Christian D

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: 398066
patrickJMT

We introduce the rule of sum (addition rule) and rule of product (product rule) in counting.
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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: 9877
TheTrevTutor

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.

Views: 22292
The Organic Chemistry Tutor

Word Application of using the Product Rule

Views: 784
Teresa Hartman

© Copyright 2017, Neha Agrawal. All rights reserved.
Product Rule, Quotient Rule, Chain Rule and Standard Formulas of Differentiation.
This video is Part 2 of the CBSE class XII 12th chapter- Continuity and Differentiability.
Also, a part of CBSE class XI 11th Limits and Derivatives
Please subscribe to my channel at
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Link to Differentiability (Continuity and Differentiability Part-1)
https://youtu.be/g09gNmO6M40
CHANNEL PLAYLIST FOR CONTINUITY
https://www.youtube.com/playlist?list=PLTa2m6WeLW_8KsyD5M3LoY9YxMMcRok75
CHANNEL PLAYLIST FOR MATRICES
https://www.youtube.com/playlist?list=PLTa2m6WeLW_9J9Jif5iQMFZ5aaGymwk-M
CHANNEL PLAYLIST FOR Inverse Trigonometric Functions
https://www.youtube.com/playlist?list=PLTa2m6WeLW_-esFJBOyg225Dh-9wQi_D6
DETERMINANTS
https://youtu.be/bnaKGsLYJvQ To find Determinant of a 2X2 and 3X3 matrix
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Views: 21573
Neha Agrawal Mathematically Inclined

A crazy hard Calc I worksheet that has chain rules nested inside other chain rules, product rules and quotient rules.

Views: 3686
Brian Stonelake

Here's some practice for choosing between the chain rule and product rule when the problem doesn't tell you which rule to use (like in a unit exam or final exam).
If you're studying for a test on derivatives and you don't know which differentiation rules to use to take the derivative of a given function, check out these eight practice problems for identifying whether to use the chain rule or the product rule.
Good luck!
www.INeedToPassCalculus.com
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INeedToPassCalculus

This calculus video tutorial explains how to find the derivative of composite functions using the chain rule. It also covers a few examples and practice problems on the product and quotient rule.
Here is a list of topics:
1. Product Rule - Derivative of x^2e^x and x^4 sinx
2. Derivative of Exponential and Trigonometric Functions
3. Product Rule - f(x)g(x)h(x)
4. Quotient Rule Derivative of Fractions and Rational Functions
5. Derivative of Radical Functions and The Square Root of X
6. Chain Rule - Derivative of Composite Functions h(x) = f(g(x))
7. f'(g(x))g'(x)
8. dy/dx = dy/du and du/dx
9. Chain Rule with Trigonometric Functions - sine, cosine, tangent and secant - sin, cos, tan, sec
10. Evaluating Derivatives of Composite functions using a table of data

Views: 25540
The Organic Chemistry Tutor

A few practice derivatives involving the product rule.

Views: 61
dmk1182

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: 60102
patrickJMT

This video lesson goes over three examples of using the chain rule where the algebra involved in finishing the problem can be rather challenging if your algebra skills are weak. Be patient... with practice these types of problems will become simple.

Views: 75225
Jim Barnard

Working on derivatives in Calculus? We solve your Calculus Problems! Let us be your online Calculus Tutor! Calculate the derivative of a function that is the product of the square root of x and e^x. Sorry for the glitchy-ness on this one.

Views: 45
SolveMyMathHW

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
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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: 28926
NancyPi

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.
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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

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NancyPi

You find an easy way to memorize the product and the quotient rules. Also, we do review on tangent line problems in Calculus 1

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Hoa Dinh

Here we have a play with Sine.

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That English Mathematician

Welcome to lecture 11 of Math 205 - Elements of Calculus.
In tonight's lecture we start by reminding ourselves of the ever important rules of derivatives--the ones we know so far, and then jump into a word problem that we need to use the first and second derivative to solve--a motion problem. The problem here is one of free fall, a typical problem you would see in a physics 1 course the first week.
We then move on to some other important derivative rules: the product rule--which we use to differentiate products of functions, and the quotient rule--which we use to differentiate quotients (or divisions) of functions.
We derive the rules and then go through some examples and tips of when not to use them. It's sometimes as important to know when not to do something as when to do it.
In our next lecture, we will look at the chain rule.

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Jhevon Smith

When I first circled the "2y" I drew over top of the plus symbol. The "-2y" in the answer should actually be positive (this does not change the problem fundamentally).

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Zach Cresswell

Examples using the Chain Rule
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/chain_rule_1?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

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Khan Academy

Chain rule helps us to differentiate "composite function". In other words, according to chain rule the derivative of f[g(x)] = f'[g(x)] • g'(x)
For example : Cos(logx) is a composite function because it can be constructed as f[g(x)] for f(x)= Cos x and g(x) = log x
Also, know when to use chain rule vs product rule, we tried to cover chain rule problems with simple chain rule formula and double chain rule formula (calculus).

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Skill Ark

For free notes and practice problems, visit the Calculus course on http://www.flippedmath.com/
Lesson 3.2 Product and Quotient Rule

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The Algebros