Limits and the Power Rule

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July 28th 2009, 06:25 PM
drkidd22

Limits and the Power Rule

I did this one using the Power Rule

$<br /> f(x)=\frac{(x^10-x^2)}{x^3}<br />$

And I Get

$<br /> \frac{10x^9-2x}{3x^2}<br />$

$<br /> \frac{10x^8-2}{3x}<br />$

$<br /> \frac{2(5x^8-1)}{3x}<br />$

I'm supposed to find the derivative. Is that it to this?
July 28th 2009, 06:38 PM
ANDS!

$<br /> f(x)=\frac{(x^10-x^2)}{x^3}<br />$

Should this be:

$<br /> F(x)=\frac{x^{10}-x^2}{x^3}<br />$

We are actually using the quotient rule here (which is really the power rule, and implicit differentiation but whatever):

$F'(x)=\frac{[f'(x)][g(x)]-[f(x)][g'(x)]}{[g(x)]^2}$

In this equation

$f(x)=(x^{10}-x^2)$
$g(x)=x^3$

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