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

解

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

\frac{2}{4 x + y}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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