Derivatives of Composite Functions - Chain Rule, Product & Quotient Rule
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- Опубліковано 27 вер 2024
- 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
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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...
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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...
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
Derivatives - Formula Sheet: bit.ly/4dThzf1
Derivatives - Formula Sheet: bit.ly/4dThzf1
Final Exams and Video Playlists: www.video-tutor.net/
Honestly don’t know what I would do without this UA-cam channel
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Exactly :|
*Agreed*
Amen brother
Same here😂
Hello everyone coming back to review for midterms. I wish you luck on your weary travels.
Edit: Also thank you for all your hard work and dedication to teach anyone willing to look up your videos. Greatly appreciated!
How can I when you belong to me but I belong to them
Erm what the sigma
i swear this guy could just do every teacher on earth's job without a sweat. He's honestly one of the biggest reasons im passing maths.
european person eh. glad to see you doing well brotha.
Just wanna say thank you for all of your videos! You are saving my life in calc during quarantine :) literally learn more in an hour of your videos than I do in a week of classes :0
Yea, Ikr...
Same here, this is sooo helpful
P
I couldn't agree more the way it is broken down is so amazing.
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.
Thank you!
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..
Watching all of your calc videos before my 2 quizzes and test. Hopefully, I'll do well.
How did you do? =D
how'd you do gang?
This content is changing the career trajectory of hundreds of thousands of people, thanks.
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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.
Same here 😳😳
no way what’re the chances
@@mkorkrish probably not that high
Woww many people learning derivatives in this time
1:05 am😂😂
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
yeah i wa like wtff is going on im i hearing right 😅
Shows all the types of questions seen in AP tests great job
52:01 you forget f’(1) is not 3 it is actually -3
And the answer is 34/4
heard this channel from my classmates and this first video i watched is pretty informative. i now know why they all learned the lesson fast 😩
chain rule 18:00
robintuition thanks bruh
THANKS :)
Thank you!
Thanks
you are the teacher who every student wants thank you very much.
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!
composite function starts from 18:13
This is really helpful. Thank you. Commenting just to help the algorithm.
I have an indescribable desire to learn things above my grade level (as of writing im in 9th) and i cant begin to tell you how good this video is. You are very good at writing it all out so if i make an error i see exactly where it was, along with a cohesive and understandable explanation
im proud of u (: never let this intellectual curiosity fade-it will carry you through life
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Same bro, even I am in 9th grade and I am learning calc to be ahead everyone!!! If I start now, I won't face much problem in the future
review your video at time"37.08", a power 2 went missing at some point
i also realized that
Me too
@51:40 you forgot a negative f'(1) is -3 not 3
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for 37:06 , tan(5x^2 + 8 )should have square , tan^2(5x^2 +8) :D
Thank you ( this channel) for existing.
The way this guy talks is nice and soothing
Great video! Your videos are enough to understand any topic.
Pls I would love u to upload hyperbolic derivatives cos u are my only reliable source of learning 😔 plsss
This was extremely helpful, thank you!
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My differentiation skills after watching this video >>>> I can literally do mental calculations now.
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...
Chain Rule happens at 18:00
careful hes a hero
thank you bro
U make my life easy thank u for helping me really
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)
thanks for all your videos on calc. I literally learn more with them.
Great video! Shows a lot of good info.
I think the answer of tan³(5x²+8) should be 30xsec²(5x²+8)[tan(5x²+8)]², correct me if I'm wrong.
thank u so much, am studying for my exams are tomorrow appreciate the teaching
You are the best, thanks for all your efforts to make a great videos. You are my favorite during my journey at College.
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Alway!!!!
If you’re asked to find the y value for the equation of the tangent line how would you do it if you have the slope already and they give you the x value
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?
You are best bro
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.
How you doing buddy, sorry n0 buddy responded to you
thank you teacher
You always help me thank you
In the final answer for the composite chain rule, it should be tan^2(5x^2+8)
You made an error. 52:29 it was supposed to be 36/4 which then h(1)=9
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?
Thanks a bunch!👍👍
gracias :) podrias hacer analisis de funciones por favor
So nice
1 thing I notice is that in my calc class, the equations are NEVER this simple. And I can NEVER find any complex product chain rule examples online
Lots of love from Pakistan ❤️❤️❤️
ahhhhh thank you so muchhhhh
Thank you so much 😊
When your midterm is 10 questions in 75mins so you have 7.5mins to do problems that take you 30 mins each to do.
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
I was really thinking about that 15:00
thank you very much
dast xos vere good
Great thanks 👍
thank you.
at 51:52 u forgot to carry the negative . it should be -3 wich makes h'(x) 36/4 wich is 9
Could you make a video on first principles?
12:11 why don’t you simplify the squared brackets?
you're my king
good video
58:46 is 2(-3) not 2(3)
f' of 1 is equal to -3
Watching in Master Economics 🙄!!
THANK YOU
36:00 isn't a derivative of tan sex^2?
at 36:37 the answer is missing a ^2 on the tangent
big sis help me i just want to know becuase I'm confused at 35:05 why there is a 2x next to the cos when the outside is just sin
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.
Thanks 👍
Watching 00:15Am
16:24 I don't understand why root x multiplied 1 multiplied root x ≠ 1 root x and root x are cancelled and 1 is left
1 times anything doesnt change it whatsoever. 3 times 3 times 1 is still 9. rootx times rootx times one is still just x (rootx times rootx = x. then x times 1 still x)
cheers chears.
Tysm 😭
Which is this software ?
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DX - D GENERATION X
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
Excuse 37:09 power of 2
But thanks anyway learnt
18:12
35:49
uh, where did the power of 2 go at 37:08?
The tan function should be squared tan^2 in the final answer
Watching this at 3:13am
39:47 he said quotiant rule instead of power rule
thankyou, I thought I was going crazy, waiting for him to turn it into a fraction lmao
43:38 - Personal Bookmark
So, u substitution proves the chain rule.