(\partial)/(\partial x)(1/(x-a))

解

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

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

解答ステップ

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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