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.