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Math Help - derivitive help!

  1. #1
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    derivitive help!

    Please help! I just can't get through this problem and I really need someone to tell me what I need to do.
    The problem is as follows f(x) 1/ (root)x; and we're using the formula of limit as delta x approaches 0; of f(x+deltax) - f(x) / (all over) delta x.; I'm unsure of how to start this problem, so any help would be so useful! thank you!!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: derivitive help!

    We are told to use first principles to find the derivative of f(x)=\frac{1}{\sqrt{x}} hence:

    f'(x)\equiv\lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}=\lim_{\Delta x\to0}\frac{\frac{1}{\sqrt{x+\Delta x}}-\frac{1}{\sqrt{x}}}{\Delta x}

    Your goal is to rewrite the expression so that you can substitute zero for \Delta x and not get division by zero. I would begin by combining the terms in the numerator with a common denominator, then rationalize the resulting numerator. See what you get. Post your work if your get stuck.
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