Q. If $y = 2^{x}.3^{2x - 1\ },\ then\frac{d^{2}y}{dx^{2}}\$is equal to
A) $(log\ 2)(log\ 3)$
B) $(log\ 18)$
C) $(\log{18^{2})}\ y^{2}$
D) ${(\log{18)}}^{2\ }y$
Explanation
(d)
Given, $y = 2^{x}.3^{2x - 1}$
$\Rightarrow \ \frac{dy}{dx} = 2^{x}.3^{2x - 1}2\log{3 + 3^{2x - 1}.2^{x}\log 2}\ \$
$= 2^{x}3^{2x - 1}\log 18 = y\log 18$
$\Rightarrow \ \frac{d^{2}y}{dx^{2}} = \frac{dy}{dx}\log{18\ }\$
$= y{(\log{18)}}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.