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Beliebt Rechnen >

derivative (x+2)/(x^2-4)

Lösung

ableitung von

\frac{x + 2}{x ^{2} - 4}

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(d^2y)/(dx^2)=sin(2x)

\frac{d ^{2} y}{d x ^{2}} = sin (2 x)

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inverselaplace 1/(s+4)

in v erse l a pl a ce \frac{1}{s + 4}

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

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

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

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