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

解

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

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

解答ステップ

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

定数を除去:

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

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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