# Thread: Differentiation from first principles

1. ## Differentiation from first principles

2x^2 - x - 8

i get to

4xdeltax + 2(deltax)^2 - deltax

the 2(deltax)^2 part is confusing me I get the answer 4x but it's supposed to be 4x - 1

thanks for any help

2. $\lim_{h\to 0}\frac{2(x+h)^{2}-(x+h)-8-(2x^{2}-x-8)}{h}$

Expanding the top and we get:

$\lim_{h\to 0}\frac{2x^{2}+4xh+2h^{2}-x-h-8-2x^{2}+x+8}{h}$

Note that many of the terms in the top cancel one another and we are left with:

$\lim_{h\to 0}\frac{4xh+2h^{2}-h}{h}$

$\lim_{h\to 0}4x+2h-1$

See what's left?. The derivative of $2x^{2}-x-8$

3. When you divide 4xdeltax + 2(deltax)^2 - deltax by deltax

you get 4x +2deltax - 1

letting delta x -> 0 you get 4x -1

4. It's the -1 that I dont't get, am I to assume -deltax divided by deltax is -1

5. -2/2 = -1

-f/f = -1

-anything/anything = -1

-dx/ddx = -1