(\partial)/(\partial x)((x-1)/(x+1))

解

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

\frac{2}{( x + 1 ) ^{2}}

解答ステップ

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

商の法則を適用:

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

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

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

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

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

簡素化

\frac{1 \cdot ( x + 1 ) - 1 \cdot ( x - 1 )}{( x + 1 ) ^{2}} : \frac{2}{( x + 1 ) ^{2}}

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