derivative of sqrt(x-\sqrt{y)}

解

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

\frac{2 y - \frac{d y}{d x}}{4 y x - y}

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 x - y} \frac{d}{d x} (x - y)

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

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

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

簡素化

\frac{1}{2 x - y} (1 - \frac{\frac{d y}{d x}}{2 y}) : \frac{2 y - \frac{d y}{d x}}{4 y x - y}

= \frac{2 y - \frac{d y}{d x}}{4 y x - y}