How would I find the derivative of x^2 + 3x using the definition of the derivative?

Answer 1

d/dx x^2+3x = 2x+3

Answer 2

the derivative of a function f(x) is
Limit [f(x+h) - f(x)]/h
h--> 0

so derivative of x^2 + 3x =
Lim[(x+h)^2 + 3(x+h) - x^2 - 3x]/h =
h--> 0
Lim [2hx + h^2 + 3h]/h =
h--> 0
Lim [2x + h + 3\]
h--> 0
= 2x + 3