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)

H (x) = f (x) / g (x)

Use the quotient rule.

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

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

h ' (1) = [ 3 * (-4) - 4 * (-3) ] / (3) ^2 = [-12 + 12] / 9 = 0

Answer: 0