(\partial)/(\partial x)((x-1)y^2e^{xy})

解

\frac{\partial}{\partial x} ((x - 1) y^{2} e^{x y})

y^{2} (e^{x y} + e^{x y} y (x - 1))

解答ステップ

\frac{\partial}{\partial x} ((x - 1) y^{2} e^{x y})

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 x} ((x - 1) e^{x y})

積の法則を適用:

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

f = x - 1, g = e^{x y}

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

\frac{\partial}{\partial x} (x - 1) = 1

\frac{\partial}{\partial x} (e^{x y}) = e^{x y} y

= y^{2} (1 \cdot e^{x y} + e^{x y} y (x - 1))

簡素化

= y^{2} (e^{x y} + e^{x y} y (x - 1))