(\partial)/(\partial x)((e^{xy})/(x+1))

解

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

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

解答ステップ

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

y

を定数として扱う

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

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