prime of f help

Question

what is: f '(-1) when you have the following information:

f(x) = x^11 * h(x)

h(-1) = 4

h ' (-1) = 7

im not sure how to find the f ' (-1) - I tried to find it myself but im having a lot of issues and I keep getting it incorrect. i'm so lost.

Answer 1

f(x) = x¹¹·h(x)

f '(x) if the first derivative of f(x) (df(x)/dx ). Since f(x) is the product of two other functions (x¹¹ and h(x)), use the Product Rule to find the derivative (f ') of f(x):

f '(x) = d(x¹¹)/dx · h(x) + x¹¹·dh(x)/dx

f '(x) = 11x¹⁰·h(x) + x¹¹·h'(x)

f '(-1) = 11(-1)¹⁰·h(-1) + (-1)¹¹·h'(-1)

Can you finish it from here?