# Thread: Limits and the Power Rule

1. ## Limits and the Power Rule

I did this one using the Power Rule

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

And I Get

$
\frac{10x^9-2x}{3x^2}
$

$
\frac{10x^8-2}{3x}
$

$
\frac{2(5x^8-1)}{3x}
$

I'm supposed to find the derivative. Is that it to this?

2. $
f(x)=\frac{(x^10-x^2)}{x^3}
$

Should this be:

$
F(x)=\frac{x^{10}-x^2}{x^3}
$

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

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