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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\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)

Vereinfache

\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}}

\frac{d}{d x} (x sinh (x) - 8 cosh (x))

x \to \infty lim (- 5^{x})

d er i v a t i v e cos (8 x)

x \to a lim (e^{f (x)})

d er i v a t i v e y = sec^{2} (3 x)