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Beliebt Rechnen >

derivative of cos^{-2}(x)

Lösung

\frac{d}{d x} (cos^{- 2} (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (cos^{- 2} (x))

Vereinfache

cos^{- 2} (x) : sec^{2} (x)

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

Wende die Kettenregel an:

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

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

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

= 2 sec (x) sec (x) tan (x)

Vereinfache

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

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

Graph

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