Business Calculus Question

Question

Given that

𝑓(𝑥)=(ℎ(𝑥))^5

ℎ(−1)=3

ℎ′(−1)=6



Calculate 𝑓′(−1).

Answer 1

By using the chain rule, the derivative of f(x) is

f'(x)=5*h(x)^4 * h'(x)

This quantity can be evaluated at x=-1 and it reads

f'(-1)=5*h(-1)^4*h'(-1)

Since h(-1)=3 and h'(-1)=6, we finally have

f'(-1)=5*3^4*6=5*27*6=2430

Best,

Davide