derivative of ln(((x+2)/(x^2)))

解

\frac{d}{d x} (ln (\frac{( x + 2 )}{x ^{2}}))

\frac{- x - 4}{x ( x + 2 )}

解答ステップ

\frac{d}{d x} (ln (\frac{( x + 2 )}{x ^{2}}))

連鎖法則を適用:

\frac{1}{\frac{x + 2}{x ^{2}}} \frac{d}{d x} (\frac{x + 2}{x ^{2}})

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

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

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

簡素化

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

= \frac{- x - 4}{x ( x + 2 )}