(\partial)/(\partial x)(arccos(x/y))

解

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

- \frac{1}{y ^{2} - x ^{2}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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