What is (\partial)/(\partial x)(ln|x|) ?

The answer to (\partial)/(\partial x)(ln|x|) is 1/x

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(\partial)/(\partial x)(ln|x|)

\frac{\partial}{\partial x} (ln ∣ x ∣)

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln ∣ x ∣)

Apply the chain rule:

\frac{1}{∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

= \frac{1}{∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

\frac{\partial}{\partial x} (∣ x ∣) = \frac{x}{∣ x ∣}

= \frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣}

Simplify

\frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣} : \frac{1}{x}

= \frac{1}{x}

What is (\partial)/(\partial x)(ln|x|) ?
The answer to (\partial)/(\partial x)(ln|x|) is 1/x