+Answer:
The derivative is 2x + 2.
Step-by-step explanation:
The definition of the derivative is the limit of
[ f(x + h)^2 - f(x)] / h when h ---> 0.
For f(x) = x^2 + 2x:
Derivative = the limit as h --> 0 of f(x)
= [ (x + h)^2 + 2(x + h) - (x^2 + 2x)] / h
= [x^2 + 2hx + h^2 + 2x + 2h - x^2 - 2x] / h
= (2hx + 2h + h^2) / h
= 2x + 2 + h
The h can be neglected
So it is 2x + 2.
