If $f (x) = \frac{1}{x}$ $f(x)= 1/x$ and $g (x) = \frac{1}{x}$ $g(x) = 1/x$ , what is $f'(g(x))$ ?

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Answer 1 · 2016-12-01T23:46:21

$-x^2$

I'll assume no error in the statement of the question.

$f'(x) = -1/x^2$

Therefore,

$f'(g(x)) = -1/(g(x))^2 = -1/(1/x)^2 = -x^2$

If f(x)= 1/x f(x)=1xf(x)= 1/x and g(x) = 1/x g(x)=1xg(x) = 1/x , what is f'(g(x)) f'(g(x)) ?