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Beliebt Rechnen >

derivative of (2x+5/(x^2-1))

Lösung

\frac{d}{d x} (\frac{2 x + 5}{x ^{2} - 1})

Lösung

\frac{- 2 x ^{2} - 10 x - 2}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 5}{x ^{2} - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x + 5 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 2 x + 5 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (2 x + 5) = 2

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

= \frac{2 ( x ^{2} - 1 ) - 2 x ( 2 x + 5 )}{( x ^{2} - 1 ) ^{2}}

Multipliziere aus

2 (x^{2} - 1) - 2 x (2 x + 5) : - 2 x^{2} - 10 x - 2

= \frac{- 2 x ^{2} - 10 x - 2}{( x ^{2} - 1 ) ^{2}}

Graph

Beliebte Beispiele

derivative f(x)=2x^3+1

d er i v a t i v e f (x) = 2 x^{3} + 1

tangent f(x)=-3x^4

t an g e n t f (x) = - 3 x^{4}

derivative y=(cos(7x))^x

d er i v a t i v e y = (cos (7 x))^{x}

kgv (x+6)/5 ,sqrt(|x|)

l c m \frac{x + 6}{5}, ∣ x ∣

derivative 40ln(3x+1)

d er i v a t i v e 40 ln (3 x + 1)