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Thread: Find the derivative using the definition only!

  1. #1
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    Find the derivative using the definition only!

    How would you show that the derivative of $\displaystyle f(x) = \frac{1}{\sqrt{x}}$ is equal to $\displaystyle \frac{1}{2\sqrt{x^3}}$ for $\displaystyle x>0$ , using the definition of a derivative??

    I started and got lost in the calculation...

    I have to start with the following
    $\displaystyle | \frac{\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{c}}}{x-c} + \frac{1}{2\sqrt{c^3}} |$ and show I can make it less than $\displaystyle \epsilon$ , which is just the definition

    I know I have $\displaystyle |x-c|<\delta$ to play with... can anyone help me out? this is due tomorrow so the more you can give me the better lol thanks
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  2. #2
    Super Member Random Variable's Avatar
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    If you're looking to find the derivative from the definition, check out this thread: http://www.mathhelpforum.com/math-he...ve-answer.html

    But it looks like you're trying to prove the existence of a limit.
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  3. #3
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    thanks that works
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