What is the derivative of x^3 - x^2 + x + 1 from first principles?

The derivative of a function f(x) from first principles is
f'(x) = `lim_(h->0)[f(x + h) - f(x)]/h`

Here f(x) =
x^3 - x^2 + x + 1

f'(x) = `lim_(h->0) [(x + h)^3 -
(x + h)^2 + (x + h) + 1 - (x^3 - x^2 + x + 1)]/h`

=>
f'(x) = `lim_(h->0)[x^3 + 3x^2h + 3xh^2 + h^3 - x^2 - h^2 - 2xh + x + h + 1 - x^3
+ x^2 - x - 1]/h`

=> f'(x) =
`lim_(h->0)[3x^2h + 3xh^2 + h^3 - h^2 - 2xh +
h]/h`

=> f'(x) = `lim_(h->0) 3x^2 + 3xh + h^2
- h - 2x + 1`

=> 3x^2 - 2x +
1

The derivative of f(x) = x^3 - x^2 + x + 1
is 3x^2 - 2x + 1