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Beliebt Rechnen >

derivative y=(2x-3)/(3x+1)

Lösung

ableitung von

y = \frac{2 x - 3}{3 x + 1}

Lösung

\frac{11}{( 3 x + 1 ) ^{2}}

Schritte zur Lösung

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

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

\frac{d}{d x} (3 x + 1) = 3

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

Multipliziere aus

2 (3 x + 1) - 3 (2 x - 3) : 11

= \frac{11}{( 3 x + 1 ) ^{2}}

Graph

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