d/(dt)(({r}(t))(cos(5t)))

Lösung

\frac{d}{d t} ((r (t)) (cos (5 t)))

cos (5 t) \frac{d}{d t} (r (t)) - 5 sin (5 t) r (t)

Schritte zur Lösung

\frac{d}{d t} ((r (t)) (cos (5 t)))

Wende die Produktregel an:

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

f = r (t), g = cos (5 t)

= \frac{d}{d t} (r (t)) cos (5 t) + \frac{d}{d t} (cos (5 t)) r (t)

\frac{d}{d t} (cos (5 t)) = - sin (5 t) \cdot 5

= \frac{d}{d t} (r (t)) cos (5 t) + (- sin (5 t) \cdot 5) r (t)

Vereinfache

= cos (5 t) \frac{d}{d t} (r (t)) - 5 sin (5 t) r (t)

f a c t or x^{3} - 2^{2} + 4 x + 112

f a c t or (x - 2)^{2} + 6 (x - 2) + 9

f a c t or n r - 6 n + m r - 6 m

f a c t or x^{2} + x - x^{3} y - y

f a c t or b^{6} - 6 b^{4} + 12 b^{2} - 8