Differentiation Question 373
Question: If f be a polynomial, then the second derivative of $ f(e^{x}) $ is
[Karnataka CET 1999]
Options:
A) $ {f}’(e^{x}) $
B) $ {f}’’(e^{x})e^{x}+{f}’(e^{x}) $
C) $ {f}’’(e^{x})e^{2x}+{f}’’(e^{x}) $
D) $ {f}’’(e^{x})e^{2x}+{f}’(e^{x})e^{x} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ y=f(e^{x}) $
Therefore $ \frac{dy}{dx}={f}’(e^{x})e^{x} $
$ \frac{d^{2}y}{dx^{2}}={f}’’(e^{x}).e^{x}.e^{x}+e^{x}.{f}’(e^{x}) $ = $ f’’(e^{x}).e^{2x}+f’(e^{x}).e^{x} $ .
BETA
