d/(da)(sec(a)tan(a)cos(a)*csc(a))

Lösung

\frac{d}{d a} (sec (a) \cdot tan (a) \cdot cos (a) \cdot csc (a))

- csc^{2} (a) sec (a) tan (a) + cot (a) (- sec (a) + 2 sec^{3} (a))

Schritte zur Lösung

\frac{d}{d a} (sec (a) tan (a) cos (a) csc (a))

Vereinfache

sec (a) tan (a) cos (a) csc (a) : cot (a) sec (a) tan (a)

= \frac{d}{d a} (cot (a) sec (a) tan (a))

Wende die Produktregel an:

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

f = cot (a), g = sec (a) tan (a)

= \frac{d}{d a} (cot (a)) sec (a) tan (a) + \frac{d}{d a} (sec (a) tan (a)) cot (a)

\frac{d}{d a} (cot (a)) = - csc^{2} (a)

\frac{d}{d a} (sec (a) tan (a)) = - sec (a) + 2 sec^{3} (a)

= (- csc^{2} (a)) sec (a) tan (a) + (- sec (a) + 2 sec^{3} (a)) cot (a)

Vereinfache

= - csc^{2} (a) sec (a) tan (a) + cot (a) (- sec (a) + 2 sec^{3} (a))

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