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Beliebt Rechnen >

derivative f(x)=(x^2-1)/(2x+2)

Lösung

ableitung von

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

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{1}{2}

Graph

Beliebte Beispiele

derivative f(x)=4x^4-5x^3+2x-3

d er i v a t i v e f (x) = 4 x^{4} - 5 x^{3} + 2 x - 3

derivative of x/(a^2sqrt(a^2+x^2))

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\int_{1}^{4} x d x

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\int e^{- 5 x} x d x