(\partial)/(\partial t)((x)(2t^3-6t^2))

解

\frac{\partial}{\partial t} ((x) (2 t^{3} - 6 t^{2}))

x (6 t^{2} - 12 t)

解答ステップ

\frac{\partial}{\partial t} ((x) (2 t^{3} - 6 t^{2}))

x

を定数として扱う

定数を除去:

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

= x \frac{\partial}{\partial t} (2 t^{3} - 6 t^{2})

和/差の法則を適用:

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

= x (\frac{\partial}{\partial t} (2 t^{3}) - \frac{\partial}{\partial t} (6 t^{2}))

\frac{\partial}{\partial t} (2 t^{3}) = 6 t^{2}

\frac{\partial}{\partial t} (6 t^{2}) = 12 t

= x (6 t^{2} - 12 t)