derivative of ln((4x^2-9/(2x-3)))

解

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

\frac{2}{2 x + 3}

解答ステップ

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

簡素化

ln (\frac{4 x ^{2} - 9}{2 x - 3}) : ln (2 x + 3)

= \frac{d}{d x} (ln (2 x + 3))

連鎖法則を適用:

\frac{1}{2 x + 3} \frac{d}{d x} (2 x + 3)

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

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

= \frac{1}{2 x + 3} \cdot 2

簡素化

\frac{1}{2 x + 3} \cdot 2 : \frac{2}{2 x + 3}

= \frac{2}{2 x + 3}