Calculating derivative using formal definition tricky

Mar 2017
358
3
Massachusetts
Can someone guide me in terms of finishing off the derivative computation that I have started below? Help is greatly appreciated!

IMG_20190615_201408 (1).jpg
 
Feb 2015
2,255
510
Ottawa Ontario
Wouldn't it be easier/shorter if you let v = sqrt(4 + h) ?
 
Jun 2013
1,151
614
Lebanon
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Jun 2013
1,151
614
Lebanon
\(\displaystyle \frac{2-\sqrt{4+h}}{h\sqrt{4+h}}\)

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

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

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