The definition of the derivative is: If $\displaystyle f(x) = \frac{1}{x^2}$ then
$\displaystyle f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h}$
So try doing that and come back and tell us how you did. We can help you if you still need help.
Tell me what f(x+h) and f(x) are, then tell post what $\displaystyle \frac{f(x+h) - f(x)}{h}$. Once you have all that you should be able to simplify things and take the derivative.
So, It's $\displaystyle 2x+h/(x^2(x+h)^2$
$\displaystyle 2x/(x^2)(x^2)$
$\displaystyle 2/x^3$
No. You have made a careless mistake in the numerator. Go back, check your work, find the mistake. Hint: You know what the final answer is meant to be, don't you ....?