Let f(x) be a polynomial in x. Then the second order derivative of $f\left(e^x\right)$ with respect to x, is
Answer & explanation
Correct answer: option 4
Let $\phi(x)=f\left(e^x\right)$ Then,
$\phi'(x)=f'\left(e^x\right) . e^x$
$\Rightarrow \phi''(x)=f''\left(e^x\right) . e^x . e^x+f'\left(e^x\right) . e^x$
$=f''\left(e^x\right) . e^{2 x}+f'\left(e^x\right) . e^x$