1. ## Derivative problem

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.

2. 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.
You're missing a term. It should be (in red)

$\displaystyle =\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h - \color{red}{x^3}}{h}$

3. Doh!