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

解

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

\frac{2}{2 x + 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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