Answer to Question #1939 in Calculus for Abhilash

Question

Find h'(1) given that f(1) = -5, f '(1) = 2, g(1) = 3, and g'(1) = 2

h(x) = f(x)/g(x)

h'(1) =

Answer 1

If h(x) = f(x)/g(x), then
h'(x) = {f'(x)g(x) - g'(x)f(x)}/g²(x)
Therefore
h'(1) = {f'(1)g(1) - g'(1)f(1)}/g²(1) = {2*3 - 2*(-5)}/3² = 16/9