We know that f'(x) and f"(x) respectively denote the first derivative and second derivative of a given function f(x) with respect to x.
If P is the inverse function of S, and P'(x)=e
x2; then:
2*S(x)*S'(x) + eS(x)2*S"(x) = ?
I wish to acknowledge the superb analytical prowess of JayDeeKay whose short yet comprehensive methodology has forced me to replace my solution with his resolution of the problem under reference.