(\partial)/(\partial y)(sqrt(5x+4y))

解

\frac{\partial}{\partial y} (5 x + 4 y)

\frac{2}{5 x + 4 y}

解答ステップ

\frac{\partial}{\partial y} (5 x + 4 y)

x

を定数として扱う

連鎖法則を適用:

\frac{1}{2 5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

= \frac{1}{2 5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

\frac{\partial}{\partial y} (5 x + 4 y) = 4

= \frac{1}{2 5 x + 4 y} \cdot 4

簡素化

\frac{1}{2 5 x + 4 y} \cdot 4 : \frac{2}{5 x + 4 y}

= \frac{2}{5 x + 4 y}