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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(dy)/(dt)=y*ln(t),y(e)=200

\frac{d y}{d t} = y \cdot ln (t), y (e) = 200

limit as x approaches 2 of (-x)/((2-x))

x \to 2 lim (\frac{- x}{( 2 - x )})

integral of e^{x+7e^x}

\int e^{x + 7 e^{x}} d x

derivative of sqrt(3x^2-4)

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

integral of-2/3 (1-x)^{3/2}(1)

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