(\partial)/(\partial x)(sqrt(x/y))

解

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

\frac{1}{2 x y}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= \frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y}

簡素化

\frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y} : \frac{1}{2 x y}

= \frac{1}{2 x y}