# Find derivative using the definition of the derivative as a limit

$$f(x) = \frac{1} {\sqrt{x}}$$

find $f'(x)$ using the definition of the derivative as a limit.

I know that

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

as $\delta$ goes to $0$.

Where do I go from here?