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Math Help - Find f'(x) using the definition of the derivative?

  1. #1
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    Oct 2009
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    Find f'(x) using the definition of the derivative?

    using the definition of the derivative find:

    f(x) = 2 / sqrt(x)


    any help is appreciated!



    I got stuck right after:

    f'(x) = lim (h--> 0) (2/ sqrt(x+h) - 2/ sqrt(x)) / h


    I just need to know where to go after this.

    Do I find the lcm of sqrt(x+h) and sqrt (x)? What is the lcm and what do I need to multiply both denominators by?
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    Here are the first few steps:

    \begin{aligned}<br />
\frac{d}{dx}\left(\frac{2}{\sqrt{x}}\right)&=\lim_  {\small h\rightarrow 0}\frac{1}{h}\left(\frac{2}{\sqrt{x+h}}-\frac{2}{\sqrt{x}}\right)\\<br />
&=\lim_{\small h\rightarrow 0}\frac{2}{h}\frac{\sqrt{x}-\sqrt{x+h}}{\sqrt{x}\sqrt{x+h}}.<br />
\end{aligned}

    Hint: What can be done to the second fraction?
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