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Beliebt Rechnen >

d/(dθ)(sec(θ)tan(θ))

Lösung

\frac{d}{d θ} (sec (θ) tan (θ))

Lösung

- sec (θ) + 2 sec^{3} (θ)

Schritte zur Lösung

\frac{d}{d θ} (sec (θ) tan (θ))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (θ), g = tan (θ)

= \frac{d}{d θ} (sec (θ)) tan (θ) + \frac{d}{d θ} (tan (θ)) sec (θ)

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

\frac{d}{d θ} (tan (θ)) = sec^{2} (θ)

= sec (θ) tan (θ) tan (θ) + sec^{2} (θ) sec (θ)

Vereinfache

sec (θ) tan (θ) tan (θ) + sec^{2} (θ) sec (θ) : - sec (θ) + 2 sec^{3} (θ)

= - sec (θ) + 2 sec^{3} (θ)

Graph

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