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

解

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

\frac{1}{x + c t}

解答ステップ

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

c, t

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (2 x + 2 c t) = 2

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

簡素化

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

= \frac{1}{x + c t}