How do you solve a derivative using its definition: (f(x+h)-f(x))/h

can you do this one for me as an example:
f(x)= 2x^2 +3x

f(x) = 2x² + 3x

lim h->0 (f(x + h) - f(x)) / h
lim h->0 (2(x + h)² + 3(x + h) - (2x² + 3x)) / h
lim h->0 ((2x² + 4xh + 2h²) + (3x + 3h) - 2x² - 3x) / h
Combine like terms now. You'll see that a few things cancel out
lim h->0 (4xh + 2h² + 3h) / h
Now divide h from everything on top
lim h->0 4x + 2h + 3
Now plug in 0 for h
4x + 3

(f(x+h)-f(x))/h=
2(x+h)^2+3x+3h-2x^2-3x/h =
2x^2+4xh+2h^2+3x+3h-2x^2-3x/h =
4x+2h+3 as h>>>0
4x+3