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Beliebt Rechnen >

derivative of (sec(2x)^7)

Lösung

\frac{d}{d x} ((sec (2 x))^{7})

Lösung

14 sec^{7} (2 x) tan (2 x)

Schritte zur Lösung

\frac{d}{d x} ((sec (2 x))^{7})

Wende die Kettenregel an:

7 (sec (2 x))^{6} \frac{d}{d x} (sec (2 x))

= 7 (sec (2 x))^{6} \frac{d}{d x} (sec (2 x))

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

= 7 (sec (2 x))^{6} sec (2 x) tan (2 x) \cdot 2

Vereinfache

7 sec^{6} (2 x) sec (2 x) tan (2 x) \cdot 2 : 14 sec^{7} (2 x) tan (2 x)

= 14 sec^{7} (2 x) tan (2 x)

Graph

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