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

解

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

- \frac{1}{x ln ^{2} ( \frac{x}{2} )}

解答ステップ

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

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

= - \frac{1}{( ln ( \frac{x}{2} ) ) ^{2}} \cdot \frac{1}{x}

簡素化

- \frac{1}{ln ^{2} ( \frac{x}{2} )} \cdot \frac{1}{x} : - \frac{1}{x ln ^{2} ( \frac{x}{2} )}

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