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Math Help - derivates

  1. #1
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    derivates

    Find the derivate of p(x)= (3x)^1/2
    using the alternative formula for the derivate
    f ' (x)= lim f(z)-f(x)/z-x
    z>x

    my answer was 1/2(3x)^1/2
    but its wrong
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lilheadbaby1
    Find the derivate of p(x)= (3x)^1/2
    using the alternative formula for the derivate
    f ' (x)= lim f(z)-f(x)/z-x
    z>x

    my answer was 1/2(3x)^1/2
    but its wrong
    \frac{f(z)-f(x)}{z-x}=\frac{(3z)^{1/2}-(3x)^{1/2}}{z-x}
    <br />
=(3z)^{1/2}\frac{(1-(x/z)^{1/2})}{z(1-x/z)}<br />

    <br />
=\left( \frac{3}{z} \right)^{1/2} \frac{1-(x/z)^2}{(1+(x/z)^{1/2})(1-(x/z)^{1/2})}

    <br />
=\left( \frac{3}{z} \right)^{1/2} \frac{1}{(1+(x/z)^{1/2})}

    So:
    <br />
\lim_{z \rightarrow x}\frac{f(z)-f(x)}{z-x}=\left( \frac{3}{x} \right)^{1/2} \frac{1}{2}= \frac{\sqrt{3}}{2} x^{-1/2}<br />


    RonL
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