(\partial)/(\partial x)(ln(k/x))

解

\frac{\partial}{\partial x} (ln (\frac{k}{x}))

- \frac{1}{x}

解答ステップ

\frac{\partial}{\partial x} (ln (\frac{k}{x}))

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{1}{x}