(\partial)/(\partial t)(te^{st})

解

\frac{\partial}{\partial t} (t e^{s t})

e^{t s} + e^{t s} t s

解答ステップ

\frac{\partial}{\partial t} (t e^{s t})

s

を定数として扱う

積の法則を適用:

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

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

= \frac{\partial}{\partial t} (t) e^{s t} + \frac{\partial}{\partial t} (e^{s t}) t

\frac{\partial}{\partial t} (t) = 1

\frac{\partial}{\partial t} (e^{s t}) = e^{s t} s

= 1 \cdot e^{s t} + e^{s t} s t

簡素化

= e^{t s} + e^{t s} t s