The function f(x) is differentiable. The function h(x) is defined as

Question

h(x) = f(x)/x

If f(1) =9 and f '(1)=10, what is h '(1)?

Answer 1

Hi Alejandro,

First find h'(x) by following the quotient rule for derivatives

h(x) = f(x) / x

h'(x) = (x f'(x) - f(x) (1)) / (x²)

Now to get h'(1) just evaluate h'(x) at x = 1. f(1) and f'(1) are both given by the problem, for x just plug in 1.