Find the second order derivatives of the function.

Let $y=\sin (\log x)$

Then,

$\frac{d y}{d x}=\frac{d}{d x}[\sin (\log x)]=\cos (\log x) \cdot \frac{d}{d x}(\log x)=\frac{\cos (\log x)}{x}$

$\therefore \frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left[\frac{\cos (\log x)}{x}\right]$

$=\frac{x \cdot \frac{d}{d x}[\cos (\log x)]-\cos (\log x) \cdot \frac{d}{d x}(x)}{x^{2}}$

$=\frac{x \cdot\left[-\sin (\log x) \cdot \frac{d}{d x}(\log x)\right]-\cos (\log x) \cdot 1}{x^{2}}$

$=\frac{-x \sin (\log x) \cdot \frac{1}{x}-\cos (\log x)}{x^{2}}$

$=\frac{-[\sin (\log x)+\cos (\log x)]}{x^{2}}$