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Math Help - Derivative from first principles

  1. #1
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    Derivative from first principles

    Use first principles to find \frac{dy}{dx} if \frac{x^2}{3}.

    I've never used the first principles to differentiate a fraction. Could someone please help me with the above and supply correct working out. All help will be appreciated.
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  2. #2
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    Quote Originally Posted by Joker37 View Post
    Use first principles to find \frac{dy}{dx} if \frac{x^2}{3}.

    I've never used the first principles to differentiate a fraction. Could someone please help me with the above and supply correct working out. All help will be appreciated.
    HI

    y=\frac{1}{3}x^2

     <br />
\frac{dy}{dx}=2(\frac{1}{3})x^{2-1}<br />
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    HI

    y=\frac{1}{3}x^2

     <br />
\frac{dy}{dx}=2(\frac{1}{3})x^{2-1}<br />
    No, no...you have to use first principles to differentiate it.
    Last edited by mr fantastic; November 13th 2009 at 09:55 PM.
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  4. #4
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    Quote Originally Posted by Joker37 View Post
    No, no...you have to use first principles to differentiate it.
    oh ok

    \frac{d}{dx}(\frac{x^2}{3})=\frac{1}{3}\frac{d}{dx  }(x^2)

     <br />
\frac{1}{3}\lim_{\delta{x}\rightarrow 0}[\frac{(x+\delta{x})^2-x^2}{\delta{x}}]<br />

    \frac{1}{3}\lim_{\delta \rightarrow 0}[\frac{x^2+2x\delta{x}+(\delta{x})^2-x^2}{\delta{x}}]

    \frac{1}{3}\lim_{\delta{x}\rightarrow 0}(2x+\delta{x})

     <br />
=\frac{2x}{3}<br />
    Last edited by mr fantastic; November 13th 2009 at 09:55 PM.
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