d/(dt)(e^tcos(t)-e^tsin(t))

解

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

- 2 e^{t} sin (t)

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= e^{t} cos (t) - e^{t} sin (t) - (e^{t} sin (t) + cos (t) e^{t})

簡素化

e^{t} cos (t) - e^{t} sin (t) - (e^{t} sin (t) + cos (t) e^{t}) : - 2 e^{t} sin (t)

= - 2 e^{t} sin (t)