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

解

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

- \frac{1}{x}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{1}{x}