(\partial)/(\partial u)((u-v)/(u+v))

解

\frac{\partial}{\partial u} (\frac{u - v}{u + v})

\frac{2 v}{( u + v ) ^{2}}

解答ステップ

\frac{\partial}{\partial u} (\frac{u - v}{u + v})

v

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 u} ( u - v ) ( u + v ) - \frac{\partial}{\partial u} ( u + v ) ( u - v )}{( u + v ) ^{2}}

\frac{\partial}{\partial u} (u - v) = 1

\frac{\partial}{\partial u} (u + v) = 1

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

簡素化

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

= \frac{2 v}{( u + v ) ^{2}}