Find F'(a) and G'(a)

Question

Let F(x) = (x^3) and G(x) = (f(x))^3 and suppose that

a^2 = 12, f(a) = 2, f'(a) = 15, f'(a^3) = 15

Find F'(a) and G'(a).

Answer 1

First, let's find F'(x):

F'(x) = 3x² ----> F'(a) = 3a² = 3(12) = 36

Now, let's find G'(x):

G'(x) = 3(f(x))²f'(x), by chain rule. ----> G'(a) = 3(f(a))²f'(a) = 3(2)²(15) = 3(4)(15) = 3(60) = 180