d/(dt)(2e^tsin(t))

解

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

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

\frac{d}{d t} (e^{t}) = e^{t}

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

= 2 (e^{t} sin (t) + cos (t) e^{t})