(\partial)/(\partial y)(cos(y/x))

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

= - sin (\frac{y}{x}) \frac{1}{x}

簡素化

- sin (\frac{y}{x}) \frac{1}{x} : - \frac{sin ( \frac{y}{x} )}{x}

= - \frac{sin ( \frac{y}{x} )}{x}