derivative t^3e^tt

解

導関数

t^{3} e^{t} t

e^{t} t^{4} + 4 t^{3} e^{t}

解答ステップ

\frac{d}{d t} (t^{3} e^{t} t)

簡素化

t^{3} e^{t} t : e^{t} t^{4}

= \frac{d}{d t} (e^{t} t^{4})

積の法則を適用:

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

f = e^{t}, g = t^{4}

= \frac{d}{d t} (e^{t}) t^{4} + \frac{d}{d t} (t^{4}) e^{t}

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

\frac{d}{d t} (t^{4}) = 4 t^{3}

= e^{t} t^{4} + 4 t^{3} e^{t}