lim h --> 0 of x^3 = [(x+h)^3 - x^3]/h

= [(x+h)(x+h)(x+h) - x^3]/h

= [x^3 + x^2 h + 2 x^2 h + 2 x h^2 + x h^2 + h^3 - x^3]/h

cancel the x^3 and the h's with the one in the bottom

= x^2 + 2 x^2 + 2 x h + x h + h^2

plug in 0 for h

= x^2 + 2 x^2

combine like terms

= 3 x^2

I hope that helps