(\partial)/(\partial y)(xye^{x+y})

解

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

x (e^{x + y} + e^{x + y} y)

解答ステップ

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

x

を定数として扱う

定数を除去:

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

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

積の法則を適用:

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

f = y, g = e^{x + y}

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

\frac{\partial}{\partial y} (y) = 1

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

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

簡素化

= x (e^{x + y} + e^{x + y} y)