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Math Help - calculate g'(a) using definition of derivative

  1. #1
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    calculate g'(a) using definition of derivative

    can someone help me calculate g'(a) for g(x) = x^(2/3) using g'(a) = lim h-->0 [(x+h)^(2/3)-x^(2/3)]/h ? Thanks for the help!
    Last edited by sdh2106; September 1st 2010 at 03:45 PM.
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  2. #2
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    recommend using the alternate definition ...

    \displaystyle g'(a) = \lim_{x \to a} \frac{g(x) - g(a)}{x - a}<br />

    \displaystyle g'(a) = \lim_{x \to a} \frac{x^{2/3} - a^{2/3}}{x - a}

    \displaystyle g'(a) = \lim_{x \to a} \frac{(x^{1/3} - a^{1/3})(x^{1/3} + a^{1/3})}{(x^{1/3} - a^{1/3})(x^{2/3} + a^{1/3}x^{1/3} + a^{2/3})}

    \displaystyle g'(a) = \lim_{x \to a} \frac{x^{1/3} + a^{1/3}}{x^{2/3} + a^{1/3}x^{1/3} + a^{2/3}} = \frac{2}{3a^{1/3}}
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  3. #3
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    thanks again man...that was very clever.
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