Originally Posted by

**evanator** Hi there,

There is no forum for basic calculus, so I will have to post in the university-level forum. I have been trying to refresh my maths for the last few months (I had forgotten everything, right down to how to do long division.) and I feel as if I have been making good progress.

I have a question about a very simple differentiation exercise:

Using the formula

$\displaystyle f'(x) = \displaystyle\lim_{\delta x \to 0} \frac{f(x + \delta x) -f(x)}{\delta x}$

find the derivative of $\displaystyle \frac{1}{x^2}$

Here is my attempt at a solution:

$\displaystyle f(x + \delta x) = \frac{1}{(x + \delta x)^2}$

$\displaystyle f(x + \delta x) - f(x) = \frac{1}{x^2 + 2 \delta x + (\delta x)^2} - \frac{1}{x^2}$

..............