Question #1939

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) =

Expert's answer

If h(x) = f(x)/g(x), then

h'(x) = {f'(x)g(x) - g'(x)f(x)}/g^{2}(x)

Therefore

h'(1) = {f'(1)g(1) - g'(1)f(1)}/g^{2}(1) = {2*3 - 2*(-5)}/3^{2} = 16/9

h'(x) = {f'(x)g(x) - g'(x)f(x)}/g

Therefore

h'(1) = {f'(1)g(1) - g'(1)f(1)}/g

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