I need help with this problem in Real Analysis please, and please make it legible. I often can't read handwriting.

Exercise 4.3.3. Let / C R be an open interval, let ce / and let f: / - R be a function. Suppose that f is differentiable at c. Let f- = f . f. Using only the definition of derivatives and Lemma 4.2.2, prove that [f-]'(c) = 2f(c).f'(c). Do not use any other theorems about differentiation, such as Theorem 4.3.1 or Theorem 4.3.3.Lemma 4.2.2. Let I C R be an open interval, let c E I and let f : I - R be a function. Then f is differentiable at c if and only iff(cth) - f(c) lim h-0 h exists, and if this limit exists it equals f(c)