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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of ((2x^3-x))/(x^4-x^2-25)

\int \frac{( 2 x ^{3} - x )}{x ^{4} - x ^{2} - 25} d x

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

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

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

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

integral of 1/((2x+3y)^2)

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

integral of sin^2(3xco)s^23x

\int sin^{2} (3 x co) s^{2} 3 x d x