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) = ?
(In reply to
Maybe the way? by e.g.)
By definition, for each real x: P(S(x)) = x
Differentiate, using the Chain rule: P′(S(x))S′(x) = 1
Therefore: exp (S(x)^2) * S′(x) = 1 .......... Eq (1)
Differentiate, using the Chain and Product rules:
S′′(x) * exp (S(x)^2) + S′(x) * exp (S(x)^2) * 2*S(x) * S′(x) = 0
Subsitute from Eq (1): S′′(x) * exp (S(x)^2) + 2*S(x)S′(x) = 0
So the required answer is Zero.
Edited on February 19, 2015, 10:11 am
re: Maybe the way? yes it is!
