(\partial)/(\partial x)((x(v-b))/(r(x,v)))

解

\frac{\partial}{\partial x} (\frac{x ( v - b )}{r ( x , v )})

(v - b) \frac{1 \cdot r ( x , v ) - \frac{\partial}{\partial x} ( r ( x , v ) ) x}{r ( x , v ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{x ( v - b )}{r ( x , v )})

b, v

を定数として扱う

定数を除去:

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

= (v - b) \frac{\partial}{\partial x} (\frac{x}{r ( x , v )})

商の法則を適用:

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

= (v - b) \frac{\frac{\partial}{\partial x} ( x ) r ( x , v ) - \frac{\partial}{\partial x} ( r ( x , v ) ) x}{r ( x , v ) ^{2}}

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

= (v - b) \frac{1 \cdot r ( x , v ) - \frac{\partial}{\partial x} ( r ( x , v ) ) x}{r ( x , v ) ^{2}}