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

解

導関数

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

\frac{6 - x}{x ( - x + 3 )}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x ^{2}}{3 - x}) = \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

= \frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

簡素化

\frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}} : \frac{6 - x}{x ( - x + 3 )}

= \frac{6 - x}{x ( - x + 3 )}