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

Lösung

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

- \frac{24 x ( x ^{2} + 1 )}{( x ^{2} - 1 ) ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

- 2 \cdot \frac{( - 6 x ) ( x ^{2} - 1 ) ^{3} - 6 x ( x ^{2} - 1 ) ^{2} ( - 3 x ^{2} - 1 )}{( ( x ^{2} - 1 ) ^{3} ) ^{2}} : - \frac{24 x ( x ^{2} + 1 )}{( x ^{2} - 1 ) ^{4}}

= - \frac{24 x ( x ^{2} + 1 )}{( x ^{2} - 1 ) ^{4}}

d er i v a t i v e (x - 5) (x + 4) (x + 6)

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

\int_{0}^{\infty} u^{2} e^{- u} d u

\frac{\partial}{\partial y} (z - x^{2} + y^{2})

d er i v a t i v e - 3 e^{x^{5}}