Let ‘f ’ be a polynomial then {f(ex)}′′ is | MATH - DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS | SolveeIt | Solveeit

Today, August 19

Question

Let ‘f ’ be a polynomial then {f(e^x)}′′ is

A

f ′′(e^x)e^x + f ′(e^x)

B

f ′′(e^x)e^2x + f ′′(e^x)e^x

C

f ′′(e^x)

D

f ′′(e^x) e^2x + f ′(e^x) e^x

Answer

f ′′(e^x) e^2x + f ′(e^x) e^x

Explanation

Solution

y = f(e^x) then y ′ = f ′(e^x) e^x

⇒ y″ = f ″(e^x)e^x. e^x + e^x f ′(e^x)