If the solve the problem

Question:

If $y=\left|\log _{e} x\right|$, find $\frac{d^{2} y}{d x^{2}}$

Solution:

Given:

$y=\left|\log _{e} x\right| \forall x>0$

$y=\log _{e} x$

$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{\mathrm{x}}=\mathrm{x}^{-1}$

$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=(-1) \mathrm{x}^{-2}$

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