derivative of (-y/x)

解

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

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

解答ステップ

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

簡素化

\frac{- y}{x} : - \frac{y}{x}

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

簡素化

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