derivative y=(ln|x+8|)^7

Lösung

ableitung von

y = (ln ∣ x + 8 ∣)^{7}

\frac{7 ln ∣ x + 8 ∣ ^{6}}{x + 8}

Schritte zur Lösung

\frac{d}{d x} ((ln ∣ x + 8 ∣)^{7})

Wende die Kettenregel an:

7 (ln ∣ x + 8 ∣)^{6} \frac{d}{d x} (ln ∣ x + 8 ∣)

= 7 (ln ∣ x + 8 ∣)^{6} \frac{d}{d x} (ln ∣ x + 8 ∣)

\frac{d}{d x} (ln ∣ x + 8 ∣) = \frac{1}{x + 8}

= 7 (ln ∣ x + 8 ∣)^{6} \frac{1}{x + 8}

Vereinfache

7 ln ∣ x + 8 ∣^{6} \frac{1}{x + 8} : \frac{7 ln ∣ x + 8 ∣ ^{6}}{x + 8}

= \frac{7 ln ∣ x + 8 ∣ ^{6}}{x + 8}

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