(\partial)/(\partial y)(sin(x/y))

解

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

- \frac{x cos ( \frac{x}{y} )}{y ^{2}}

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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