Differentiate y=x^2 from first principles

y=x²dy/dx= Lim_h-->0( ((x+h)²-x²) / (x+h-x) )dy/dx= Lim_h-->0( (x² + 2hx + h² - x²) / h )dy/dx= Lim_h-->0( (h² + 2hx) / h )dy/dx= Lim_h-->0( h + 2x )dy/dx= Lim_h-->0( h ) + 2xdy/dx= 2x