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Beliebt Rechnen >

derivative of sec^3(4x)

Lösung

\frac{d}{d x} (sec^{3} (4 x))

Lösung

12 sec^{3} (4 x) tan (4 x)

Schritte zur Lösung

\frac{d}{d x} (sec^{3} (4 x))

Wende die Kettenregel an:

3 (sec (4 x))^{2} \frac{d}{d x} (sec (4 x))

= 3 (sec (4 x))^{2} \frac{d}{d x} (sec (4 x))

\frac{d}{d x} (sec (4 x)) = sec (4 x) tan (4 x) \cdot 4

= 3 (sec (4 x))^{2} sec (4 x) tan (4 x) \cdot 4

Vereinfache

3 sec^{2} (4 x) sec (4 x) tan (4 x) \cdot 4 : 12 sec^{3} (4 x) tan (4 x)

= 12 sec^{3} (4 x) tan (4 x)

Graph

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