Derive the quotient rule. Show that the difference quotient for f/g is 

Before letting h approach zero, rewrite this quotient using the trick of subtracting and adding g(x) f (x) in the numerator.

1 f(x + h) h[g(x + h) - f(x) g(x) = g(x)f(x +h)-f(x) g(x + h) g(x + h)g(x)h