What is the Derivative

i know it sounds stupid but what's the Derivative ?
where did it come from i know that drevative is the change
but if we say dy/dx = ( y2-y1/x2-x1 )
so what is the first dy/dx' will be ?
and what the second dy/dx" will be ?
thank you =]

f (x) is a function of x

f `(x) is defined as the derivative of f (x)

f ` (x) is defined as :-

lim
h-->0 [ f(x + h) - f(x) ] / h

Examples
----------------
f (x) = a x^n
f ` (x) = n a x^(n - 1)

f (x) = 3 x^5
f ` (x) = 15 x^4

Hi
You know what,everytime i study maths,i ask to many things to myself.Where the hell this came from??Lecturers teach us all this things but they even don't know where the hell it came from))
Maybe some smart lecturers from harvard University can answer this question!

dy-dx