derivative (ln(x))^6

Lösung

ableitung von

(ln (x))^{6}

\frac{6 ln ^{5} ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{6})

Wende die Kettenregel an:

6 (ln (x))^{5} \frac{d}{d x} (ln (x))

= 6 (ln (x))^{5} \frac{d}{d x} (ln (x))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 6 (ln (x))^{5} \frac{1}{x}

Vereinfache

6 ln^{5} (x) \frac{1}{x} : \frac{6 ln ^{5} ( x )}{x}

= \frac{6 ln ^{5} ( x )}{x}