(\partial)/(\partial y)(sqrt(3x+2y))

解

\frac{\partial}{\partial y} (3 x + 2 y)

\frac{1}{3 x + 2 y}

解答ステップ

\frac{\partial}{\partial y} (3 x + 2 y)

x

を定数として扱う

連鎖法則を適用:

\frac{1}{2 3 x + 2 y} \frac{\partial}{\partial y} (3 x + 2 y)

= \frac{1}{2 3 x + 2 y} \frac{\partial}{\partial y} (3 x + 2 y)

\frac{\partial}{\partial y} (3 x + 2 y) = 2

= \frac{1}{2 3 x + 2 y} \cdot 2

簡素化

\frac{1}{2 3 x + 2 y} \cdot 2 : \frac{1}{3 x + 2 y}

= \frac{1}{3 x + 2 y}