d/(dt)(6cos^3(t))

Lösung

\frac{d}{d t} (6 cos^{3} (t))

- 18 cos^{2} (t) sin (t)

Schritte zur Lösung

\frac{d}{d t} (6 cos^{3} (t))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d t} (cos^{3} (t))

Wende die Kettenregel an:

3 (cos (t))^{2} \frac{d}{d t} (cos (t))

= 3 (cos (t))^{2} \frac{d}{d t} (cos (t))

\frac{d}{d t} (cos (t)) = - sin (t)

= 6 \cdot 3 (cos (t))^{2} (- sin (t))

Vereinfache

= - 18 cos^{2} (t) sin (t)