Find h'(1) for the function h(x)=f(x)f(x) where f is a function such that f(1)=4 and f'(1)=1

Answer 1

By the formula for the derivative of a product

h'(x) = f(x)f'(x) + f'(x)f(x) = 2f(x)f'(x)

Substituting given numbers

h'(1) = 2 x 4 x 1 = 8