(\partial)/(\partial y)(2sqrt(xy))

解

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

\frac{x}{y}

解答ステップ

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

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{x}{y}