What is the derivative of ln|x-3| ?

The derivative of ln|x-3| is 1/(x-3)

What is the first derivative of ln|x-3| ?

The first derivative of ln|x-3| is 1/(x-3)

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\frac{d}{d x} (ln ∣ x - 3 ∣)

\frac{1}{x - 3}

Solution steps

\frac{d}{d x} (ln ∣ x - 3 ∣)

Apply the chain rule:

\frac{1}{∣ x - 3 ∣} \frac{d}{d x} (∣ x - 3 ∣)

= \frac{1}{∣ x - 3 ∣} \frac{d}{d x} (∣ x - 3 ∣)

\frac{d}{d x} (∣ x - 3 ∣) = \frac{x - 3}{∣ x - 3 ∣}

= \frac{1}{∣ x - 3 ∣} \cdot \frac{x - 3}{∣ x - 3 ∣}

Simplify

\frac{1}{∣ x - 3 ∣} \cdot \frac{x - 3}{∣ x - 3 ∣} : \frac{1}{x - 3}

= \frac{1}{x - 3}

What is the derivative of ln|x-3| ?
The derivative of ln|x-3| is 1/(x-3)
What is the first derivative of ln|x-3| ?
The first derivative of ln|x-3| is 1/(x-3)