(\partial)/(\partial x)(arccot(x/y))

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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