(\partial}{\partial y}(ln(\frac{x^2)/y))

解

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))

- \frac{1}{y}

解答ステップ

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))

x

を定数として扱う

連鎖法則を適用:

\frac{1}{\frac{x ^{2}}{y}} \frac{\partial}{\partial y} (\frac{x ^{2}}{y})

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

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

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

簡素化

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

= - \frac{1}{y}