(x/(x^3-1))^'

Lösung

(\frac{x}{x ^{3} - 1})^{^{'}}

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

Schritte zur Lösung

(\frac{x}{x ^{3} - 1})^{'}

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

x^{'} = 1

(x^{3} - 1)^{'} = 3 x^{2}

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

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

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

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

d er i v a t i v e e^{2 x} + 1

\int_{0}^{\infty} \frac{e ^{x}}{1 + e ^{x}} d x

t an g e n t f (x) = 4 x^{2} + 3 x + 6, (- 4, 58)

cr i t i c a l f (x) = I n (2 x + 1)