How to do chain rule differentiation problems (calculus 1 homework help)

We will go over 17 chain rule differentiation problems. These questions are from Stewart Calculus, sect 3.4. They will range from basic to kind of hard. Some of the problems also require the product rule or the quotient rule.

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Thanks to Lazarus Isaac Ng for the Timestamps
0:00 (1+x+x^2)^99
1:36 (5x^6+2x^3)^4
4:21 (x+1/x)^5
5:42 e^(tan θ)
6:17 2^(t^3)
8:04 1/cbrt(x^2-1)
11:29 sqrt(x+sqrt(x+sqrt(x)))
14:36 cot^2(sin θ)
17:12 tan(sec(cos t))
19:24 e^(z/(z-1))
21:14 sqrt(x/(x+1))
25:12 x^2 e^(-3x)
27:55 e^(-2x)sin(3x)
30:04 e^(at)sin(bt)
33:57 (2x-3)^4 (x^2+x+1)^5
39:17 (x^2+1)^3 (x^3+2)^6
44:23 (r^2-1)^3/(2r+1)^5
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[lazarusisaacng]

0:00 (1+x+x^2)^99
1:36 (5x^6+2x^3)^4
4:21 (x+1/x)^5
5:42 e^(tan θ)
6:17 2^(t^3)
8:04 1/cbrt(x^2-1)
11:29 sqrt(x+sqrt(x+sqrt(x)))
14:36 cot^2(sin θ)
17:12 tan(sec(cos t))
19:24 e^(z/(z-1))
21:14 sqrt(x/(x+1))
25:12 x^2 e^(-3x)
27:55 e^(-2x)sin(3x)
30:04 e^(at)sin(bt)
33:57 (2x-3)^4 (x^2+x+1)^5
39:17 (x^2+1)^3 (x^3+2)^6
44:23 (r^2-1)^3/(2r+1)^5

[AhmedAMayow]

Thanks Please 😊 🙏
make videos application of derivatives
Maximum minimum points of inflection
Concave up and Concave down for rational functions

[nidhiagrawal]

13:42 Won't the blue bracket come inside the second term of the red bracket?

[JayOnDaCob]

Watching your video in has been funny to me, I’m in precalc and now I know how to find the derivative of a decent amount of functions

[blueslime]

13:50, shouldn't the last parenthesis be inside of the first, just in front of 1/2sqrt(x+sqrt(x))?
I'm pretty sure it would

[nidhiagrawal]

cos(t) without the brackets is cost. You said the derivative of cost is negative but cost always goes up according to inflation lol 😂😂😂

[sankaralingamsivaramakrish]

6th example, does this need one more differentiation of sqrt(x), the third one?

[nidhiagrawal]

43:06 you could have factored the 2 when you were originally factoring things out.

[emmecuh]

Hey, thats my favorite derivative rule!