use limit formula to find

$\displaystyle

f'(x) = \frac{1}{x^2}

$

$\displaystyle

lim \frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}

$

$\displaystyle

lim \frac{\frac{x^2 - (x+h)(x+h)}{x^2(x+h)(x+h)}}{h}

$

$\displaystyle

lim \frac{\frac{-2xh-h^2}{x^2(x+h)(x+h)}}{h}

$

$\displaystyle

lim \frac{\frac{h(-2xh-h)}{x^2(x+h)(x+h)}}{h}

$

is this correct so far?