(\partial)/(\partial x)(sqrt(1+2x))

解

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

\frac{1}{1 + 2 x}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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