d/(dt)((x)(te^t))

解

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

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

解答ステップ

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

x

を定数として扱う

定数を除去:

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

= x \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}

= x (\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}

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

簡素化

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