derivative of sqrt(2xy)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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