d/(dy)(arctan(y/x))

解

\frac{d}{d y} (arctan (\frac{y}{x}))

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

解答ステップ

\frac{d}{d y} (arctan (\frac{y}{x}))

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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