derivative of (-2x^3-1/((x^3-1)^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int y^{6} d y

y y^{^{'}} = x (1 + y^{2})

\frac{d}{d x} (e^{e^{2 x}})

\int \frac{2 x + 1}{x ^{2} + 2 x + 65} d x

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