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Math Help - Differentiation from 1st principles

  1. #1
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    Sep 2007
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    Differentiation from 1st principles

    Can anyone see where I'm going wrong here...

    So differentiate from 1st principles.

    f(x) = sqrt(x)+1

    f'(x) = (sqrt(x+h)+1)-(sqrt(x)+1) / h

    f'(x) = x+h+1-x-1 / h(sqrt(x+h)+1)+(sqrt(x)+1)

    So cancelling terms i get,

    f'(x) = 1 / (sqrt(x+h)+1)+(sqrt(x)+1)

    f'(x) = 1 / 2sqrt(x) + 2

    This is where I'm confused, shouldn't it be

    f'(x) = 1 / 2sqrt(x)
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  2. #2
    Super Member
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    You did not expand nor rationalize correctly.

    \begin{aligned}<br />
\sqrt{x+h} + 1 - (\sqrt{x}+1) &= \sqrt{x+h} + 1 - \sqrt{x} - 1\\<br />
&= \sqrt{x+h} - \sqrt{x}<br />
\end{aligned}

    A fit conjugate would be \sqrt{x+h} + \sqrt{x}. By your way, you should've got:

    ((\sqrt{x+h}+1)-(\sqrt{x}+1))(\sqrt{x+h}+1)+(\sqrt{x}+1)) =(\sqrt{x+h}+1)^2 - (\sqrt{x}+1)^2 = \ldots
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  3. #3
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    Ah i see.. I didn't get rid of the ones... thats a stupid mistake..

    Thanks alot
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