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Beliebt Rechnen >

derivative (2x+3)/(3x-2)

Lösung

ableitung von

\frac{2 x + 3}{3 x - 2}

Lösung

- \frac{13}{( 3 x - 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 3 )}{( 3 x - 2 ) ^{2}} : - \frac{13}{( 3 x - 2 ) ^{2}}

= - \frac{13}{( 3 x - 2 ) ^{2}}

Graph

Beliebte Beispiele

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