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

Dec 1, 2016

$- {x}^{2}$

#### Explanation:

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

$f ' \left(x\right) = - \frac{1}{x} ^ 2$

Therefore,

$f ' \left(g \left(x\right)\right) = - \frac{1}{g \left(x\right)} ^ 2 = - \frac{1}{\frac{1}{x}} ^ 2 = - {x}^{2}$