What is the derivative of (ln|x+2|)^7 ?

The derivative of (ln|x+2|)^7 is (7ln|x+2|^6)/(x+2)

What is the first derivative of (ln|x+2|)^7 ?

The first derivative of (ln|x+2|)^7 is (7ln|x+2|^6)/(x+2)

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derivative of

(ln ∣ x + 2 ∣)^{7}

\frac{7 ln ∣ x + 2 ∣ ^{6}}{x + 2}

Solution steps

\frac{d}{d x} ((ln ∣ x + 2 ∣)^{7})

Apply the chain rule:

7 (ln ∣ x + 2 ∣)^{6} \frac{d}{d x} (ln ∣ x + 2 ∣)

= 7 (ln ∣ x + 2 ∣)^{6} \frac{d}{d x} (ln ∣ x + 2 ∣)

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

= 7 (ln ∣ x + 2 ∣)^{6} \frac{1}{x + 2}

Simplify

7 ln ∣ x + 2 ∣^{6} \frac{1}{x + 2} : \frac{7 ln ∣ x + 2 ∣ ^{6}}{x + 2}

= \frac{7 ln ∣ x + 2 ∣ ^{6}}{x + 2}

What is the derivative of (ln|x+2|)^7 ?
The derivative of (ln|x+2|)^7 is (7ln|x+2|^6)/(x+2)
What is the first derivative of (ln|x+2|)^7 ?
The first derivative of (ln|x+2|)^7 is (7ln|x+2|^6)/(x+2)