how do you use the chain rule?

Question

Find dy/dx.
y = x^3(2x - 7)^4

Answer 1

y'= 3x^2* (2x-7)^4 + x^3 [4(2x-7)^3*2)
y'= 3x^2* (2x-7)^4 + 8x^3 (2x-7)^3
y'= x^2(2x-7)^3 [3(2x-7) + 8x]

For the chain rule, say you had your (2x-7)^4
take f[x]= 2x-7 and n=power
(f[x])^n

Chaining for the derivative will get you
n(f[x])^n-1 * f'[x] so in your question, we get
4(2x-7)^3 * 2

Note: f[x]=2x-7
f'[x]=2

Answer 2

bring down each power in front
then take one off of each power
next multiply the derivitave of () by all of that
i believe

well the answer is 7x^2 * (2x-7)^3 * (2x-3)

Answer 3

That is chain rule and product rule. So first you would find the derivative of x^3 which is 3x^2 times (2x-7)^4 then + 8x^3(2x-7)^3.

For chain rule you move the exponent in front then lower it by one. you keep the stuff in parenthesis but then you get the derivative of it. I simplified.