Assume that f and g are differentiable functions such that f(2) = -5, f'(2) = -3, g(2) = 2, and g'(2) = 7. Given that h(x) = f(x) * g(x), find h'(2)

Answer 1

h(x) = f(x) * g(x)

h'(x) = f(x) * g'(x) + f'(x) * g(x)

h'(2) = f(2) * g'(2) + f'(2) * g(2)

= -5 * 7 + -3 * 2

= -35 + -6

= -41