Question: Let \(f\left( x \right)=\sin \left( {{e}^{x}} \right)\), f : R → R.

(a) Prove that there is a function g : R → R such that g’(x) = f(x), for each x ? R.

(b) Prove that any such function g is continuous.

(c) Prove that, if h : R →R is another such function, then h differs from g by a constant.

(d) Prove that any such function is monotone on (-∞; 0], but not on [0;∞).