Question

If $y=\cos \left(\log x\right)$, then $\frac{d^{2}y}{d{x}^2}$ $=?$

Answer 1

$y=cos\left[logx\right]$ differentiation both side with respect to X.
$\frac{dy}{dx}=-sin\left[logx\right]\times \frac{1}{x}$
again differentiation with respect to X.
$\frac{d^{2}y}{d{x}^2}=-cos\left[logx\right]\times \frac{-1}{x^2}\times \frac{1}{x}$
$\frac{d^{2}y}{d{x}^2}=cos\left[log\right]\times \frac{1}{x^3}$