I'm trying to find the derivative of $\dfrac{1}{\sqrt{x+5}}$ using $\displaystyle \lim_{h\to 0} \frac {f(x+h)-f(x)}{h}$
So,
$\begin{align*} \lim_{h\to 0} \frac{\dfrac{1}{\sqrt{x+h+5}}-\dfrac{1}{\sqrt{x+5}}}{h} &= \frac{\dfrac{\sqrt{x+5}-\sqrt{x+h+5}}{(\sqrt{x+h+5})(\sqrt{x+5})}}{h}\\\\ &= \frac{\dfrac{x+5-x-h-5}{(\sqrt{x+h+5})(\sqrt{x+5})}}{\dfrac{h}{\sqrt{x+5}}+\dfrac{h}{\sqrt{x+h+5}}} \end{align*}$
I do not know if this is correct or not.. please help. I'm stuck.