derivative of ln(3+x-x^3)

解

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

\frac{- 3 x ^{2} + 1}{3 + x - x ^{3}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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