derivative (ln|x+2|)^7

解

導関数

(ln ∣ x + 2 ∣)^{7}

\frac{7 ln ∣ x + 2 ∣ ^{6}}{x + 2}

解答ステップ

\frac{d}{d x} ((ln ∣ x + 2 ∣)^{7})

連鎖法則を適用:

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}

簡素化

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}