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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{6}{( 4 x - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (4 x - 1) = 4

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

Vereinfache

\frac{2 ( 4 x - 1 ) - 4 ( 2 x + 1 )}{( 4 x - 1 ) ^{2}} : - \frac{6}{( 4 x - 1 ) ^{2}}

= - \frac{6}{( 4 x - 1 ) ^{2}}

Graph

Beliebte Beispiele

integral of ((2x))/(x^2+1)

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derivative of (x^2/(6+sqrt(x)))