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Math Help - Finding derivative from limit definition

  1. #1
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    Finding derivative from limit definition

    Given the limit definition :

    m= \lim_{\Delta x\rightarrow 0} f(x) = (x+\Delta x)- f(x) / \Delta x

    ( / means all divided by  \Delta x) how can I find the derivative of:

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


    Step by step would be helpful.
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  2. #2
    MHF Contributor Calculus26's Avatar
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  3. #3
    Super Member Random Variable's Avatar
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     \lim_{\Delta x\rightarrow 0} \frac {\sqrt{(x+\Delta x)+2} - \sqrt {x+2}}{\Delta x}

     = \lim_{\Delta x\rightarrow 0} \frac {\sqrt{(x+\Delta x)+2} - \sqrt {x+2}}{\Delta x} \frac {\sqrt {(x+\Delta x)+2} + \sqrt {x+2}}{\sqrt{(x+\Delta x)+2}+ \sqrt {x+2}}

    and go from there
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