What is the derivative of ln|x+2| ?

The derivative of ln|x+2| is 1/(x+2)

What is the first derivative of ln|x+2| ?

The first derivative of ln|x+2| is 1/(x+2)

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\frac{d}{d x} (ln ∣ x + 2 ∣)

\frac{1}{x + 2}

Solution steps

\frac{d}{d x} (ln ∣ x + 2 ∣)

Apply the chain rule:

\frac{1}{∣ x + 2 ∣} \frac{d}{d x} (∣ x + 2 ∣)

= \frac{1}{∣ x + 2 ∣} \frac{d}{d x} (∣ x + 2 ∣)

\frac{d}{d x} (∣ x + 2 ∣) = \frac{x + 2}{∣ x + 2 ∣}

= \frac{1}{∣ x + 2 ∣} \cdot \frac{x + 2}{∣ x + 2 ∣}

Simplify

\frac{1}{∣ x + 2 ∣} \cdot \frac{x + 2}{∣ x + 2 ∣} : \frac{1}{x + 2}

= \frac{1}{x + 2}

What is the derivative of ln|x+2| ?
The derivative of ln|x+2| is 1/(x+2)
What is the first derivative of ln|x+2| ?
The first derivative of ln|x+2| is 1/(x+2)