If y=x^2log_ex, then (d^2y)/(dx^2) is equal to :

The correct answer is Option (2) → $3+2\log_e\, x$

$y=x^2\log_ex$

$\frac{dy}{dx}=2x\log_ex+x^2×\frac{1}{x}=2x\log_ex+x$

$⇒\frac{d^2y}{dx^2}=2\left(\log_ex+x^2×\frac{1}{x}\right)+1$

$=2(\log_ex+1)+1$

$=2\log_ex+3$