d/(dt)(sec(t)tan(t))

Lösung

\frac{d}{d t} (sec (t) tan (t))

- sec (t) + 2 sec^{3} (t)

Schritte zur Lösung

\frac{d}{d t} (sec (t) tan (t))

Wende die Produktregel an:

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

f = sec (t), g = tan (t)

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

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

\frac{d}{d t} (tan (t)) = sec^{2} (t)

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

Vereinfache

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

= - sec (t) + 2 sec^{3} (t)

a re a y = 5 cos (x), y = 5 sin (x), 0 \leq x \leq π

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