derivative of (xy/(sqrt(xy)))

解

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

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

解答ステップ

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

簡素化

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

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

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

簡素化

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