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

解

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

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

解答ステップ

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

積の法則を適用:

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

f = t^{2}, g = e^{t}

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

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

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

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