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Math Help - Finding the Derivative - Complex Fraction with Radicals

  1. #1
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    Finding the Derivative - Complex Fraction with Radicals

    So I've been doing good with these until this problem.

    Find f'(a)

    f(x)=\frac{8}{\sqrt{x+2}}

    This is what we have to start with.

    \frac{\frac{8}{\sqrt{a+h+2}}-\frac{8}{\sqrt{a+2}}}{h}

    I began multiplying by a common denominator to get rid of the complex fraction, then multiplied by a conjugate to get rid of the square roots. After that I don't know what to do.
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  2. #2
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    Quote Originally Posted by soad View Post
    So I've been doing good with these until this problem.

    Find f'(a)

    f(x)=\frac{8}{\sqrt{x+2}}

    This is what we have to start with.

    \frac{\frac{8}{\sqrt{a+h+2}}-\frac{8}{\sqrt{a+2}}}{h}

    I began multiplying by a common denominator to get rid of the complex fraction, then multiplied by a conjugate to get rid of the square roots. After that I don't know what to do.
    you should be up to this point ...

    8 \lim_{h \to 0} \frac{1}{h}\left(\frac{-h}{\sqrt{a+h+2} \cdot \sqrt{a+2} \left[\sqrt{a+h+2}+\sqrt{a+2}\right]}\right)

    note that the h's cancel, allowing the limit to be evaluated as ...

    -\frac{8}{(a+2) \cdot 2\sqrt{a+2}} = -\frac{4}{(a+2)^{\frac{3}{2}}}
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  3. #3
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    Okay... so the h's cancel out because it's approaching 0?

    If so, I completely understand now.
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