derivative of tan(y/x)

解

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

\frac{sec ^{2} ( \frac{y}{x} ) ( x \frac{d y}{d x} - y )}{x ^{2}}

解答ステップ

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

連鎖法則を適用:

sec^{2} (\frac{y}{x}) \frac{d}{d x} (\frac{y}{x})

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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