What is the derivative of ln|4x| ?

The derivative of ln|4x| is 1/x

What is the first derivative of ln|4x| ?

The first derivative of ln|4x| is 1/x

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\frac{d}{d x} (ln ∣ 4 x ∣)

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln ∣ 4 x ∣)

Simplify

ln ∣ 4 x ∣ : ln (4 ∣ x ∣)

= \frac{d}{d x} (ln (4 ∣ x ∣))

Apply the chain rule:

\frac{1}{4 ∣ x ∣} \frac{d}{d x} (4 ∣ x ∣)

= \frac{1}{4 ∣ x ∣} \frac{d}{d x} (4 ∣ x ∣)

\frac{d}{d x} (4 ∣ x ∣) = \frac{4 x}{∣ x ∣}

= \frac{1}{4 ∣ x ∣} \cdot \frac{4 x}{∣ x ∣}

Simplify

\frac{1}{4 ∣ x ∣} \cdot \frac{4 x}{∣ x ∣} : \frac{1}{x}

= \frac{1}{x}