Question

chain rule version y=((x+2)(3x^3+3x))^4

Answer 1

Well chain rule is just the f'g(x)g'(x). So we have to figure out which one is f(g(x)) and which one is g(x)

f(g(x)) = ((x+2)(3x^3+3x))^4

f'(g(x)) = 4((x+2)(3x^3+3x))^3

g(x) = (x+2)(3x^3+3x) which means we have to product rule.

g'(x) = (x+2)(9x^2 + 3) + (3x^3 + 3x)(2)

now we just put the parts to together: f'(g(x)) (g'(x))

d/dx (f(g(x))) = [4((x+2)(3x^3 + 3x)^3] [(x+2)(9x^2 + 3) + (3x^3 + 3x)(2)]

simplify it if you can.