I need help with this problem in Real Analysis please, and please make it legible I often can't read the handwriting. I need to solve exercise 4.3.6. and have included the reference for it.

Theorem 4.3.3 (Chain Rule). Let I, J C R be open intervals, let c E I and let f : 1- J and g: J - R be functions. Suppose that f is differentiable at c, and that g is differentiable at f(c). Then go f is differentiable at c and [go f]'(c) = 8'(f(c)) . f'(c). Before we give a proof of the Chain Rule, we want to present an attempted proof of this theorem that takes the most straightforward possible approach, though in this case the straightforward approach has a flaw. The attempted proof is "lim (gof) (x) - (go f) (c) = lim g(f(x)) - 8(f(c) ) x-c X-C = lim s(f (x)) - 8(f(c)) f(x) - f(c) f(x) - f(c) X-C = 8'(f(c)) . f(c)."Exercise 4.3.6. [Used in Section 4.3.] Explain the flaw in the attempted proof of the Chain Rule (Theorem 4.3.3) that is given prior to the correct proof. Restate the Chain Rule with modified hypotheses that would make the attempted proof into a valid proof