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Beliebt Rechnen >

derivative of (3x+5/(x^2-x))

Lösung

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

Lösung

\frac{- 3 x ^{2} - 10 x + 5}{( x ^{2} - x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 5 ) ( x ^{2} - x ) - \frac{d}{d x} ( x ^{2} - x ) ( 3 x + 5 )}{( x ^{2} - x ) ^{2}}

\frac{d}{d x} (3 x + 5) = 3

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

= \frac{3 ( x ^{2} - x ) - ( 2 x - 1 ) ( 3 x + 5 )}{( x ^{2} - x ) ^{2}}

Multipliziere aus

3 (x^{2} - x) - (2 x - 1) (3 x + 5) : - 3 x^{2} - 10 x + 5

= \frac{- 3 x ^{2} - 10 x + 5}{( x ^{2} - x ) ^{2}}

Graph

Beliebte Beispiele

integral from 0 to 3 of xsqrt(16-x^2)

\int_{0}^{3} x 16 - x^{2} d x

limit as x approaches 0 of-xln(x)-x

x \to 0 lim (- x ln (x) - x)

integral of x*sqrt(x)

\int x \cdot x d x

derivative 1/(x-1)

d er i v a t i v e \frac{1}{x - 1}

x*y^'=sqrt(x^2-2xy-y^2)+y

x \cdot y^{^{'}} = x^{2} - 2 x y - y^{2} + y