(\partial)/(\partial t)((z)(s^2t-st^{27}))

解

\frac{\partial}{\partial t} ((z) (s^{2} t - s t^{27}))

z (s^{2} - 27 s t^{26})

解答ステップ

\frac{\partial}{\partial t} ((z) (s^{2} t - s t^{27}))

z, s

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial t} (s^{2} t - s t^{27})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial t} (s^{2} t) - \frac{\partial}{\partial t} (s t^{27}))

\frac{\partial}{\partial t} (s^{2} t) = s^{2}

\frac{\partial}{\partial t} (s t^{27}) = 27 s t^{26}

= z (s^{2} - 27 s t^{26})