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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- Feb 13th 2006, 12:12 PMlilheadbaby1derivates
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 - Feb 13th 2006, 01:48 PMCaptainBlackQuote:

Originally Posted by**lilheadbaby1**

$\displaystyle

=(3z)^{1/2}\frac{(1-(x/z)^{1/2})}{z(1-x/z)}

$

$\displaystyle

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

$\displaystyle

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

So:

$\displaystyle

\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}

$

RonL