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Derivatives of Composite Functions - Chain Rule, Product & Quotient Rule
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- Опубликовано: 8 сен 2016
- 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.
Derivatives - Limit Definition: • Definition of the Deri...
Derivatives - Alternate Limit Definition: • Alternate Form of The ...
Derivatives - The Constant Rule: • The Constant Rule For ...
Derivatives - The Power Rule: • The Power Rule For Der...
Derivatives - Constant Multiple Rule: • The Constant Multiple ...
Derivatives - Polynomial Functions: • Derivatives of Polynom...
Derivatives - Sine and Cosine: • Derivative of Sine and...
Derivatives - Trigonometric Functions: • Derivatives of Trigono...
Derivatives - Limits: • Limits and Derivatives
_______________________________________________________________________________________
Derivatives - Tangent Line: • How To Find The Equati...
Derivatives - Horizontal Tangent Line: • How to Find The Point ...
The Equation of The Normal Line: • How To Find The Equati...
The Equation of The Secant Line: • How To Find The Equati...
Average and Instantaneous Velocity: • Average Velocity and I...
Instantaneous Rate of Change: • Instantaneous Rate of ...
Derivatives - Rational Functions: • Derivatives of Rationa...
Derivatives - Radical Functions: • Derivatives of Radical...
Derivatives - Fractions: • How To Find The Deriva...
Derivatives - Higher Order: • Higher Order Derivatives
_______________________________________________________________________________________
Derivatives - Simplifying: • Simplifying Derivatives
Derivatives - Product Rule - f*g: • Product Rule For Deriv...
Derivatives - Product Rule - f*g*h: • Product Rule With 3 Fu...
Derivatives - Product Rule - f*g*h*k: • Product Rule With 4 Fu...
Derivatives - Quotient Rule: • Quotient Rule For Deri...
Derivatives - Chain Rule: • Chain Rule For Finding...
Chain Rule With Trig Functions: • How To Find The Deriva...
Chain Rule - Harder Examples: • Calculus - Chain Rule ...
Chain Rule - Triple SQRT(x): • Find The Derivative Us...
Derivatives - Composite Functions: • Derivatives of Composi...
_______________________________________________________________________________________
Implicit Differentiation: • Implicit Differentiation
Derivatives - Inverse Trig Functions: • Derivatives of Inverse...
Derivatives - Exponential Functions: • Derivatives of Exponen...
Derivatives - Logarithmic Functions: • Derivative of Logarith...
Logarithmic Differentiation: • Introduction to Logari...
Derivatives - Using Logarithms: • Finding Derivatives Us...
Derivatives - Inverse Functions: • Derivatives of Inverse...
Derivatives - Differentiation Rules: • Basic Differentiation ...
Derivatives - Function Notations: • dy/dx, d/dx, and dy/dt...
Derivatives - The Reciprocal Rule: • The Reciprocal Rule an...
________________________________________________________________________________________
Introduction to Limits: • Calculus 1 - Introduct...
Introduction to Related Rates: • Introduction to Relate...
Local Maximum & Minimum: • Finding Local Maximum ...
L'Hopital's Rule: • L'hopital's rule
Optimization Problems: • Optimization Problems ...
Antiderivatives: • Antiderivatives
Calculus 1 Final Exam Review: • Calculus 1 Final Exam ...
Full-Length Exams and Worksheets: bit.ly/4990rzU
Final Exams and Video Playlists: www.video-tutor.net/
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Watching this 00:36 am
Edit 1: this is 3 years later and i love how i still get comments from my late night chemistry homies. Also i finished chemistry at the same time this comment went up and im not looking back good luck to anyone having chem exams.
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Woww many people learning derivatives in this time
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Erm what the sigma
At 37:01 you forgot to carry down that the tan function was squared, so the answer should be 30xtan^2(5x^2+8)*sec^2(5x^2+8)
Yah itx squared he 4got
ya I was confused I thought I got it wrong but..
Hi ,
At 51:55 f prime of 1 is -3 so the end result is 34/4 = 17/2 i.e. 8.5
Exactly, but he has done a great job explaining derivatives.
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Watching all of your calc videos before my 2 quizzes and test. Hopefully, I'll do well.
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Shows all the types of questions seen in AP tests great job
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You just explained this way better than the Princeton Review book did. The book has good practice problems I just find it hard to understand their explanations. Thank you so much 🙏
I can't believe I made it to the end of this video but I did. This was so helpful and I took notes on everything. The exam is next week wish me luck!
composite function starts from 18:13
39:48 Y=[5+4x]^4 [7x-x^2]^5 is a product and chain rule combined but, you mistakenly said product and quotient rule hope this will clarify the misunderstanding to future people watching this. great youtube channel to learn Math and Science
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This is really helpful. Thank you. Commenting just to help the algorithm.
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Very Nice Video
The only I want to say that at 51:55
You put 2(3) where it supposed to be 2(-3) in which will change your answer from -6+40/4 which is then equal 34/4 which is then equal to 8.5
I wanted to comment about this point also.
Sharp observation there. I also got it 8.5 (34/4). Nonetheless, Great kudos to the TUTOR of TUTORS!
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52:01 you forget f’(1) is not 3 it is actually -3
And the answer is 34/4
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chain rule 18:00
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review your video at time"37.08", a power 2 went missing at some point
i also realized that
Me too
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@51:40 you forgot a negative f'(1) is -3 not 3
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Very nicely explained.
This Good. I thought we were gonna factorization that quadratic
37:00- you forgot the squared-exponent of tan(5x+8)
It should be... 30x[tan(5x+8)]^2[sec(5x+8)]^2
But great video though☺
Yeah I noticed that too...
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Could you make a video on first principles?
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Hi! Not sure if you will see this, but thought I would try. Thank you for these videos, they are helping me a lot. Question though: @ 37:09 you give the final answer but don't include the ^2 on [tan(5x^2+8)]. Shouldn't it be 30x[tan(5x^2+8)]^2? Is there a rule that I am missing where that shouldn't be included? Thanks!!
Yeah thats a wrong answer....
30x[tan(5x^2+8)]^2[sec(5x^2+8)]^2 is what I got...Plz correct me if I am wrong
@@rafiatbm7867 Yeah that is correct
@@rafiatbm7867 Yh that’s correct which can also be written as 30xTan^2(5x+8)Sec^2(5x+8)
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for 37:06 , tan(5x^2 + 8 )should have square , tan^2(5x^2 +8) :D
Something that helped me see it wasn't just a black box where you have to follow rules without understanding them was trying it with just a power of x. The derivative of x^8 is 8x^7. What if you use the product rule to find the derivative of x^5 * x^3? f'(x) is 5x^4, g'(x) is 3x^2. So you get (5x^4 * x^3) + (x^5 * 3x^2). That's 5x^7 + 3x^7, or 8x^7, the same as if you combined them.
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You're always so gooood, but this time I think at 37:07:- you forgot to put the square above the tan(5x^2+8) in the last line.
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How to form a differential equation from y=AX^2+B/x+C/X^2 where A,B,C are orbitary constant?
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Excuse me I have a question ..... your solving the examples from calclus book for (thomas. george B . Thomas Jr . maurice D . Joel R . Hass ) book ?
No
You're my savior hehe but u forgot about the negative sign on 3 (table part) It's actually supposed to be 44/4 and so the answer is 11 not 23/2
THANK YOU
I was really thinking about that 15:00
thanks sir
25:05 why arent we taking the derivative of the 3x²-5?
I think the answer of tan³(5x²+8) should be 30xsec²(5x²+8)[tan(5x²+8)]², correct me if I'm wrong.
thank you.
At 21:15, how is this derived? That is, why dy/dx = dy/du * du/dx?
I understand the logic that follows but why does he reach this conclusion in the first place?
at 51:54 you put 3 instead of negative 3, the answer is 34/4.
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Chain Rule happens at 18:00
careful hes a hero
thank you bro
You made an error. 52:29 it was supposed to be 36/4 which then h(1)=9
I'm confused at 35:05 why there is a 2x next to the cos
at 17:40, can someone explain how the 1/2 in the numerator became 2sqrx when he moved it to the denominator
yea he made a mistake there. It's not 2*rootx on denominator, its rootx*(x+5)^2
I have a doubt, at 39:46, shouldn't the Tutor say, "The example is a combination of product rule and chain rule" instead of "The example is a combination of product rule and quotient rule". Am I missing something here?
12:11 why don’t you simplify the squared brackets?
When your midterm is 10 questions in 75mins so you have 7.5mins to do problems that take you 30 mins each to do.
Is any of what he’s saying supported by data. I mean I see him drawing a graph in a board and inspirational music playing but is this backed by studies?
I feel like 30 mins of work and 5 mins of break could work, but I think planned breaks at good “break” points is more important because if you take a break in the middle of an assignment you’re gonna spend 5-10 mins jumping back into it. If you don’t believe me try programming and stopping mid code and come back to it later lol.
uh, where did the power of 2 go at 37:08?
At 57:17 why didn’t you multiply 6 with 0. Isn’t the equation like g’(f(x)) • f’(x)? So shouldn’t we multiply 6 with 0 because it’s the f(x) inside the g. And then multiply it with f’(x) so the answer would be 0 and not 42
Watching this at 3:13am
In the final answer for the composite chain rule, it should be tan^2(5x^2+8)
36:00 isn't a derivative of tan sex^2?
18:12
35:49