derivative of ln(((2)/(3-x^2)))

解

\frac{d}{d x} (ln (\frac{( 2 )}{3 - x ^{2}}))

\frac{2 x}{3 - x ^{2}}

解答ステップ

\frac{d}{d x} (ln (\frac{( 2 )}{3 - x ^{2}}))

連鎖法則を適用:

\frac{1}{\frac{2}{3 - x ^{2}}} \frac{d}{d x} (\frac{2}{3 - x ^{2}})

= \frac{1}{\frac{2}{3 - x ^{2}}} \frac{d}{d x} (\frac{2}{3 - x ^{2}})

\frac{d}{d x} (\frac{2}{3 - x ^{2}}) = \frac{4 x}{( 3 - x ^{2} ) ^{2}}

= \frac{1}{\frac{2}{3 - x ^{2}}} \cdot \frac{4 x}{( 3 - x ^{2} ) ^{2}}

簡素化

\frac{1}{\frac{2}{3 - x ^{2}}} \cdot \frac{4 x}{( 3 - x ^{2} ) ^{2}} : \frac{2 x}{3 - x ^{2}}

= \frac{2 x}{3 - x ^{2}}