Let h(x)=xg(x), where g(x)=the inverse of f(x). find h'(5) using the that in a minute)

h(x) = x g(x)
h'(x) = x g'(x) + (1)g(x)
h'(x) = x g'(x) + g(x)

Since g(x) = f^-1(x), then
g'(x) = 1/f'(x)

h'(x) = x/f'(x) + f^-1(x)
Therefore,
h'(5) = 5/f'(5) + f^-1(5). 

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