Differentiation — Maths STD 12 Science — Question

If $y = x \log x$, then $\frac{d^2 y}{d x^2}=$ $\frac{1}{x}$
Explanation:
$y=x \log x$
Differentiating both sides,
$\frac{d y}{d x}=x \cdot \frac{d}{d x}(\log x)+\log x \cdot \frac{d}{d x}(x)$
$=x \cdot \frac{1}{x}+\log x=1+\log x$
Again differentiating w.r.t.x,
$\frac{d}{d x}\left(\frac{d y}{d x}\right)=\frac{d}{d x}(1)+\frac{d}{d x}(\log x)$
$\frac{d^2 y}{d x^2}=0+\frac{1}{x}=\frac{1}{x}$