Originally Posted by

**mathbit** This is a problem for finding the $\displaystyle f'(x)$ of $\displaystyle x^3 $ from a definition for a derivative which is derived from the definition for $\displaystyle m_{tan}$:

$\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$

So, after plugging in the function

$\displaystyle f'(x)=\lim_{h\to0}\frac{(x+h)^3-x^3}{h}$ and doing some mad Algebra, I get to this point

$\displaystyle

=\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h}{h}

$

and don't know where to go. Can anyone help?

I think that maybe I missed or am blocking this bit of Algebra. A link to a relevant online Algebra reference text would also be appreciated.