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

解

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

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

解答ステップ

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

定数を除去:

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

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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