Question

Let F(x) = f(x ^ 5) and G(x) = (f(x)) ^ 5 . You also know that a ^ 4 = 3 , f(a)=2, f^ prime (a)=13; f^ prime (a^ 5 )=2

Answer 1

We have that

$F(x)=f(x^5)$

and

$G(x)=f(x)^5$

So we have that

$F(a)=f(a^5)$

and

$G(a)=f(a)^5$

So we have that

$F^{\prime}(a)=f^{\prime}(a^5)$

and

$G^{\prime}(a)=f^{\prime}(a)^5=13^5=371293$

Then F'(a) = 2 and G'(a) = 371293.