derivative of \sqrt[3]{tan(5x})

Lösung

\frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}

Schritte zur Lösung

Wende die Kettenregel an:

\frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan (5 x))

= \frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan (5 x))

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

= \frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} sec^{2} (5 x) \cdot 5

Vereinfache

\frac{1}{3 tan ^{\frac{2}{3}} ( 5 x )} sec^{2} (5 x) \cdot 5 : \frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}

= \frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}