(\partial)/(\partial x)(ln(x/y))

解

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

\frac{1}{x}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= \frac{1}{\frac{x}{y}} \cdot \frac{1}{y}

簡素化

\frac{1}{\frac{x}{y}} \cdot \frac{1}{y} : \frac{1}{x}

= \frac{1}{x}