Question

i don't understand this problem

Let F(x)=f(x^4) and G(x)=(f(x))^4. You also know that a^3=2, f'(a)=13, f'(a^4)=15. Find F'(a) and G'(a).

Answer 1

F(x)=f(x^4)

Using the chain rule,
F'(x)=f'(x^4)*(d(x^4)/dx)=f'(x^4)*3x^3
substitute x for a and all the numerical values supplied to find F'(a).

Similarly, G(x)=(f(x))^4
Apply the chain rule successively,
G'(x)=(d/dx)(f(x))^4)
=4f(x)^3*f'(x)
So G'(a)=4f(a)^3*f'(a)
Although f'(a) is known, it is not clear to me how we can find f(a).