(\partial)/(\partial x)((y)(x^3-2y^2))

解

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

3 y x^{2}

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

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

\frac{\partial}{\partial x} (2 y^{2}) = 0

= y (3 x^{2} - 0)

簡素化

= 3 y x^{2}