derivative of (x^3+1/(x^3-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int (x - 1) 2 - x d x

x \to 3 lim (\frac{f ( x ) - f ( π )}{x - 3})

\int_{- \infty}^{\infty} x^{8} e^{- x^{9}} d x

\int - 4 x d x

\int - cos (x^{2}) d x