Rules of Differentiation

Question

If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2, then find h '(2) if h(x) = f(x) g(x). 

Options:

1. 13
2. -13
3. 7
4. -7

Answer 1

h(x) = f(x)*g(x); we will use the product rule to get h'(x)

h'(x) = f(x)*g'(x) + g(x)*f'(x) and we have all the parts for when we plug in x = 2, f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2;

so h'(2) = f(2)*g'(2) + g(2)*f'(2) and substituting from our givens, into f(x)*g'(x) + g(x)*f'(x)

h'(2) = 5*(-2) + 3*1 = -10 + 3 = -7