Having Issues with Solving Derivatives

[Nogard]

Homework Statement

Use the definition of a derivative to compute the derivative of the function at the given value.
P(t)=t^3-4, t=-2

Homework Equations

Please help me solve it in this form: f(a+h)-f(a)/h
lim
h→0

The Attempt at a Solution

(-2+h)^3-(-2^3)-4/h=(h^3-6h^2+12h-4)/h=h^2-6h+8=0-0+8=8

I am sick and tired of using the exact method the textbook gives me and getting answers that are miles off.

 

[lurflurf]

first find
P(t+h)-P(t)=((t+h)^3-4)-(t^3-4)

(-2+h)^3-(-2^3)-4/h=(h^3-6h^2+12h-4)/h=h^2-6h+8=0-0+8=8
should be
((-2+h)^3-4)-((-2^3)-4))/h=(h^3-?h^2+?h)/h=h^2-?h+?->0^2-?0+?=?
where I have replaced numbers with ? for you to fill in

 

[Nogard]

first find
P(t+h)-P(t)=((t+h)^3-4)-(t^3-4)

(-2+h)^3-(-2^3)-4/h=(h^3-6h^2+12h-4)/h=h^2-6h+8=0-0+8=8
should be
((-2+h)^3-4)-((-2^3)-4))/h=(h^3-6h^2+12h)/h=h^2-6h+12->0^2-(6)0+12=12
where I have replaced numbers with ? for you to fill in

Correct?

 

[Mark44]

Looks good.