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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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