# Thread: Calculating derivative using formal definition tricky

1. ## Calculating derivative using formal definition tricky

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

2. ## Re: Calculating derivative using formal definition tricky

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

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4. ## Re: Calculating derivative using formal definition tricky

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

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

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

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