anonymous 5 years ago the derivative of 2x^2 I need to know how to solve this using the derivative as a function... (using limits)

1. amistre64

$\lim_{h->0}\frac{f(x+h)-f(x)}{h}$

2. anonymous

I already know that formula, i need to know how to use it....

3. amistre64

$\lim\frac{2(x+h)^2-2x^2}{h}$ $\lim\frac{2(x^2+2xh+h^2)-2x^2}{h}$ $\lim\frac{2x^2+4xh+2h^2-2x^2}{h}$ $\lim\frac{\cancel{2x^2}+4xh+2h^2\cancel{-2x^2}}{h}$ $\lim\frac{4xh}{h}+\frac{2h^2}{h}$ $\lim\frac{4x}{1}+\frac{2h}{1}$

4. amistre64

if you know the formula, you know how to use it :/

5. amistre64

now, when h=0; 4x+2h = 4x

6. amistre64

when I first did these the "x" part of the function confused me a bit since they used x as part of the substituions

7. amistre64

f(x+h) should be written better as say: f(a+h) maybe so that you know to replace "x" by whats in the ( )

8. anonymous

ok, now i get it thanks alot

9. amistre64

youre welcome, and good luck :)