Differentiation Problem

Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f ' (3) = -5, f ' (1) = -4, g ' (1) = -3, g ' (3) = 2, then find h ' (1) if h(x) = f(x) / g(x).

Answer 1

Use the Quotient Rule on h(x) = f(x) / g(x):

h'(1) = [g(1)f'(1) - f(1)g'(1)] / [g(1)}^2

= [(3)(-4) - (4)(-3)] / (3)^2 = 0