# Math Help - Trouble finding basic derivatives

1. ## Trouble finding basic derivatives

I understand the formula to find derivatives, but for some reason I can't seem to get the right answer when applying said formula most of the time. Here's an example, maybe someone could walk me through step by step?

3x^2-x^3

Now I used an online derivative calculator and got the answer, but I still can't even come to that answer when I try to apply the lim (h--0) f(x+h)-f(x) over H formula. I keep getting -3x^2+2x and the correct answer is 6x-3x^2

2. Ill get you started..

So $f(x) = 3x^2 - x^3$

Now to compute the derivative we put $f(x)$ into the definition of the derivative.
that is:
$\lim_{ h\to 0} \frac{ f(x+h) - f(x)}{h}$ (the definition of a derivative)

Now.. ( $f(x)= 3x^2-x^3$ into the definition)
$\lim_{ h\to 0} \frac{ 3(x+h)^2-(x+h)^3 - (3x^2 - x^3) }{h}$

After expanding we get:

$= \lim_{ h\to 0} \frac{3(x^2+2hx+h^3)-(x^3+3x^2h+3xh^2+h^3) - 3x^2 +x^3}{h}$

Canceling terms.. and to the end of the problem...

$= \lim_{ h\to 0} \frac{6hx+3h^2-3x^2h-3xh^2-h^3}{h}$

$= \lim_{ h\to 0} 6x+3h-3x^2-3xh-h^2$

$= 6x-3x^2$