(\partial)/(\partial x)(-1/2 ln(x/a))

解

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

- \frac{1}{2 x}

解答ステップ

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{2} \frac{\partial}{\partial x} (ln (\frac{x}{a}))

連鎖法則を適用:

\frac{1}{\frac{x}{a}} \frac{\partial}{\partial x} (\frac{x}{a})

= \frac{1}{\frac{x}{a}} \frac{\partial}{\partial x} (\frac{x}{a})

\frac{\partial}{\partial x} (\frac{x}{a}) = \frac{1}{a}

= - \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a}

簡素化

- \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a} : - \frac{1}{2 x}

= - \frac{1}{2 x}