Q. If $f$ be a polynomial, then the second derivative of $f(e^{x})$ is
A) $f^{'}(e^{x})$
B) $f^{''}\left( e^{x} \right)e^{x} + f^{'}(e^{x})$
C) $f^{''}\left( e^{x} \right)e^{2x} + f^{''}(e^{x})$
D) $f^{''}\left( e^{x} \right)e^{2x} + f^{'}\left( e^{x} \right)e^{x}$
Explanation
The correct answer is Option D: $f^{''}\left( e^{x} \right)e^{2x} + f^{'}\left( e^{x} \right)e^{x}$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.