(\partial)/(\partial t)((y^2)(y-t^2+1))

解

\frac{\partial}{\partial t} ((y^{2}) (y - t^{2} + 1))

- 2 y^{2} t

解答ステップ

\frac{\partial}{\partial t} ((y^{2}) (y - t^{2} + 1))

y

を定数として扱う

定数を除去:

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

= y^{2} \frac{\partial}{\partial t} (y - t^{2} + 1)

和/差の法則を適用:

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

= y^{2} (\frac{\partial}{\partial t} (y) - \frac{\partial}{\partial t} (t^{2}) + \frac{\partial}{\partial t} (1))

\frac{\partial}{\partial t} (y) = 0

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

\frac{\partial}{\partial t} (1) = 0

= y^{2} (0 - 2 t + 0)

簡素化

= - 2 y^{2} t