Question:
If $y=\left|\log _{e} x\right|$, find $\frac{d^{2} y}{d x^{2}}$
Solution:
Given:
$y=\left|\log _{e} x\right| \forall x>0$
$y=\log _{e} x$
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\mathrm{x}}=\mathrm{x}^{-1}$
$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=(-1) \mathrm{x}^{-2}$