I'm not finding correctly the derivative of:

$\displaystyle f(x) = x^4 - 1$

I do the following:

lim h-> 0:

$\displaystyle \frac{(x+h)^4 -1 -(x^4-1)}{h}$

$\displaystyle = \frac{(x^2+h^2)^2 -x^4}{h}$

$\displaystyle = \frac{x^4 + 2x^2h^2 + h^4 - x^4}{h}$

$\displaystyle = \frac{2x^2h^2+h^4}{h}$

$\displaystyle = 2x^2h+h^3$

Then, of course, when I substitute "0" for "h", I get an answer of 0.

The correct answer is: $\displaystyle 4x^3$

Where did I go wrong?

Thank you!