Question

Let F(x)=f(x^4) and G(x)=(f(x))^4. You also know that a^3=15, f(a)=2, f′(a)=4, f′(a^4)=12. Find F′(a) and G′(a).

I don't even know where to begin.

Answer 1

It's cool. I figured it out on my own.
But for anyone in the future who needs help with a similar question:
F'(a)=f'(a^4)*4a^3
=12*4*15
=720
G'(a)=4(f(a))^3*f'(a)
=4(2)^3*4
=128
You just have to replace x with a and use the chain rule. I didn't realize it was that simple.