(\partial)/(\partial x)(x/(x-b))

解

\frac{\partial}{\partial x} (\frac{x}{x - b})

- \frac{b}{( x - b ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{x}{x - b})

b

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} ( x ) ( x - b ) - \frac{\partial}{\partial x} ( x - b ) x}{( x - b ) ^{2}}

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

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

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

簡素化

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

= - \frac{b}{( x - b ) ^{2}}