derivative of ln((2x/(x+9)))

解

\frac{d}{d x} (ln (\frac{2 x}{x + 9}))

\frac{9}{x ( x + 9 )}

解答ステップ

\frac{d}{d x} (ln (\frac{2 x}{x + 9}))

連鎖法則を適用:

\frac{1}{\frac{2 x}{x + 9}} \frac{d}{d x} (\frac{2 x}{x + 9})

= \frac{1}{\frac{2 x}{x + 9}} \frac{d}{d x} (\frac{2 x}{x + 9})

\frac{d}{d x} (\frac{2 x}{x + 9}) = \frac{18}{( x + 9 ) ^{2}}

= \frac{1}{\frac{2 x}{x + 9}} \cdot \frac{18}{( x + 9 ) ^{2}}

簡素化

\frac{1}{\frac{2 x}{x + 9}} \cdot \frac{18}{( x + 9 ) ^{2}} : \frac{9}{x ( x + 9 )}

= \frac{9}{x ( x + 9 )}