Definition+of+the+derivative+of+a+function

The definition of the derivative of a function is: Note: Dy/Dx= f '(x)

Ex: f(x)= x^2 f '(x)= lim [(x+h)^2 - x^2]/h h-->0 f '(x)= lim (x^2 + 2xh + h^2 - x^2)/h h-->0 (The x^2 and the -x^2 cancel out) f '(x)= lim h(2x+h)/h h-->0 f '(x)= lim 2x+h h-->0 (Plug in 0 for h since that is what the limit is approaching) f '(x)= 2x