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Math Help - Definition of the derivative

  1. #1
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    Definition of the derivative

    I can't get anywhere with this question, any help would be awsome:

    f(x) = srt(3x+1)
    find f'(x) using ONLY the definition of the derivative (no power laws etc)

    Starting off:

    f'(x) = lim [h->0] [f(x+h) - f(x)]/(h)]

    = lim [h->0] [sqt(3x+3h+1) - sqt(3x+1)]/h


    From here I cannot seem to get rid of the h from the bottom?
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  2. #2
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    Re: Definition of the derivative

    Multiply top and bottom by the conjugate of \sqrt{3x + 3h + 1} - \sqrt{3x+1}. The conjugate is \sqrt{3x+3h + 1} + \sqrt{3x+1}. So, you get:

    \lim_{h \to 0} \dfrac{\sqrt{3x+3h+1} - \sqrt{3x+1}}{h}\cdot \dfrac{\sqrt{3x+3h+1} + \sqrt{3x+1}}{\sqrt{3x+3h+1} + \sqrt{3x+1}}

    Now, the numerator simplifies to 3h which is divisible by h allowing you to cancel.

    To write using LaTeX, try Reply With Quote to someone else's post and see how they do it.
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