If $f(x) = 1/\sqrt{x}$, find $f^{\prime}(x)$. Please show the answer by using
$\lim_{h\to{0}}\frac{f(x+h)-f(x)}{h}.$
I know the answer by using the shortcut, but my teacher wants me to get the answer using that equation. I am stuck and I got to: $-\sqrt{x}/2x^2$ by using the $\frac{f(x+h)-f(x)}{h}$.