Find the derivative using the definition?

Question

What does it mean in Calculus when they say; find the derivative of this function using the definition. What is the definition? (I'm sure I have learned it but I can't remember what it is) A simple example would help a lot.

Answer 1

f `(x) = lim h->0 [ f(x + h) - f(x) ] / h , h ≠ 0
Example
f(x) = 3x²
f(x + h) - f(x) = 3(x + h)² = 3x² + 6hx + 3h² - 3x²
f(x + h) - f(x) = 3x² + 6hx + 3h² - 3x²
f(x + h) - f(x) = (h) (6x + 3h)
f `(x) = 6x + 3h as h--> 0
f `(x) = 6x

Answer 2

its using limit notation

lim f(x+h)-f(x)
h->0 ---------------
...................h