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

解

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

\frac{1}{2 y x}

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{1}{2 y x}