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

解

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

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

解答ステップ

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

積の法則を適用:

(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)

簡素化

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