Real Analysis Differential Proof

I seem to be having a problem understanding delta epsilon proofs so any explanations would be great if you can do this problem. Its been about 12 years since I took Calculus so I'm having to go back and review alot and proofs have always been a problem for me. I started it using the definition and h->0 but really I'm totally confused with this problem.

Suppose the f is differentiable at a and f'(a) does not = 0.

a) Using the theorem lim x->a f(x)/g(x) = L/M and the definition of the derivative, prove directly (1/f)'(a) = -f'(a)/f^2(a).

b) Use part a) and the product rule to prove the quotient rule.