Question

Assume that
f(0) = 2, f '(0) = 3, h(0) = −1, h'(0) = 7.
Calculate the derivative of the following function at
x = 0.
f(5x) · h(5x)

Answer 1

Well, the answer is 55 to anyone who views this later :)

Use the product rule to get

d/dx(f(5x)*h(5x) + d/dx(h(5x)*f(5x)
= f'(5x)*5*h(5x) (<---use chain rule, derivative of outer [f(5x)] times derivative of inner [5]) + h'(5x)*5*f(5x) (<--same, chain rule again)

Then just plug in given values and you'll get d/dx(f(5x)*h(5x)) = 55.