d/(dt)(({r}(t))(2sin(t)-e^{-t}))

解

\frac{d}{d t} ((r (t)) (2 sin (t) - e^{- t}))

\frac{d}{d t} (r (t)) (2 sin (t) - e^{- t}) + (2 cos (t) + e^{- t}) r (t)

解答ステップ

\frac{d}{d t} ((r (t)) (2 sin (t) - e^{- t}))

積の法則を適用:

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

f = r (t), g = 2 sin (t) - e^{- t}

= \frac{d}{d t} (r (t)) (2 sin (t) - e^{- t}) + \frac{d}{d t} (2 sin (t) - e^{- t}) r (t)

\frac{d}{d t} (2 sin (t) - e^{- t}) = 2 cos (t) + e^{- t}

= \frac{d}{d t} (r (t)) (2 sin (t) - e^{- t}) + (2 cos (t) + e^{- t}) r (t)