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

Jun 17, 2016

$f ' \left(g \left(x\right)\right) = 1$

#### Explanation:

As $f \left(x\right) = \frac{1}{x}$ and $g \left(x\right) = \frac{1}{x}$

$f \left(x\right) = g \left(x\right)$

and $f \left(g \left(x\right)\right) = f \left(\frac{1}{x}\right) = \frac{1}{\frac{1}{x}} = x$

Hence, $f ' \left(g \left(x\right)\right) = \frac{\mathrm{df}}{\mathrm{dg}} = 1$