# Calculating derivative using formal definition tricky

#### otownsend

Can someone guide me in terms of finishing off the derivative computation that I have started below? Help is greatly appreciated!

#### DenisB

Wouldn't it be easier/shorter if you let v = sqrt(4 + h) ?

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#### Idea

$$\displaystyle \frac{2-\sqrt{4+h}}{h\sqrt{4+h}}$$

$$\displaystyle =\frac{2-\sqrt{4+h}}{h\sqrt{4+h}}\left(\frac{2+\sqrt{4+h}}{2+\sqrt{4+h}}\right)$$

$$\displaystyle =\frac{-h}{h\sqrt{4+h}\left(2+\sqrt{4+h}\right)}$$

$$\displaystyle =\frac{-1}{\sqrt{4+h}\left(2+\sqrt{4+h}\right)}$$

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