d/(dt)(2te^t)

解

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

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

f = t, g = e^{t}

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

\frac{d t}{d t} = 1

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

= 2 (1 \cdot e^{t} + e^{t} t)

簡素化

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