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Thread: Calculating derivative using formal definition tricky

  1. #1
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    Question 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!

    Calculating derivative using formal definition tricky-img_20190615_201408-1-.jpg
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  2. #2
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    Re: Calculating derivative using formal definition tricky

    Wouldn't it be easier/shorter if you let v = sqrt(4 + h) ?
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    Re: Calculating derivative using formal definition tricky

    .
    Last edited by Idea; Jun 15th 2019 at 10:07 PM.
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  4. #4
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    Re: Calculating derivative using formal definition tricky

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

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

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

    $\displaystyle =\frac{-1}{\sqrt{4+h}\left(2+\sqrt{4+h}\right)}$
    Last edited by Idea; Jun 15th 2019 at 10:13 PM.
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