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Math Help - Finding the derivative of this function:

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    Finding the derivative of this function:

    (square root of x) - 1/ (square root of x) +1


    I know there must be some basic algebra that I'm missing, but I don't know how to handle the square roots. Any help is much appreciated in advance.


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    Quote Originally Posted by bobsanchez View Post
    (square root of x) - 1/ (square root of x) +1


    I know there must be some basic algebra that I'm missing, but I don't know how to handle the square roots. Any help is much appreciated in advance.


    Thanks
    quotient rule ...

    \frac{d}{dx} \left(\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)

    \frac{(\sqrt{x} + 1)\left(\frac{1}{2\sqrt{x}}\right) - (\sqrt{x}-1)\left(\frac{1}{2\sqrt{x}}\right)}{(\sqrt{x} + 1)^2}

    factor the numerator ...

    \frac{\left(\frac{1}{2\sqrt{x}}\right)[(\sqrt{x}+1)- (\sqrt{x}-1)]}{(\sqrt{x} + 1)^2}

    combine like terms in the numerator ...

    \frac{\left(\frac{1}{2\sqrt{x}}\right)[2]}{(\sqrt{x} + 1)^2}

    final version ...

    \frac{1}{\sqrt{x}(\sqrt{x} + 1)^2}
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