Question

Let F(x)=f(x^ 3 ) and G(x)=(f(x)) ^3 . You also know that a ^2 =4,f(a)=2,f ′ (a)=2,f ′ (a ^3 )=6 .

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

Answer 1

\[G(x)=(f(x))^3\]
\[G'(x)=3f(x)^2\times f'(x)\]

Answer 2

\[G'(a)=3f(a)^2\times f'(a)=3\times 2^2\times 2\]