derivative of ((-4x(2x-2))/(-3x^2+1))

Lösung

\frac{d}{d x} (\frac{( - 4 x ) ( 2 x - 2 )}{- 3 x ^{2} + 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{( - 4 x ) ( 2 x - 2 )}{- 3 x ^{2} + 1})

Vereinfache

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

= \frac{d}{d x} (- \frac{4 x ( 2 x - 2 )}{- 3 x ^{2} + 1})

Entferne die Konstante:

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

= - 4 \frac{d}{d x} (\frac{x ( 2 x - 2 )}{- 3 x ^{2} + 1})

Wende die Quotientenregel an:

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

= - 4 \cdot \frac{\frac{d}{d x} ( x ( 2 x - 2 ) ) ( - 3 x ^{2} + 1 ) - \frac{d}{d x} ( - 3 x ^{2} + 1 ) x ( 2 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (x (2 x - 2)) = 4 x - 2

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

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

Vereinfache

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

= - \frac{4 ( - 6 x ^{2} + 4 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

x \to - 1 lim (x - x^{3})

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

\int \frac{1}{9 x + 7} d x

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

\int (\frac{9}{x} - \frac{4}{x ^{3}}) d x