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Beliebt Rechnen >

derivative of (3x-5/(2x+4))

Lösung

\frac{d}{d x} (\frac{3 x - 5}{2 x + 4})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 5}{2 x + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 5 ) ( 2 x + 4 ) - \frac{d}{d x} ( 2 x + 4 ) ( 3 x - 5 )}{( 2 x + 4 ) ^{2}}

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

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

= \frac{3 ( 2 x + 4 ) - 2 ( 3 x - 5 )}{( 2 x + 4 ) ^{2}}

Vereinfache

\frac{3 ( 2 x + 4 ) - 2 ( 3 x - 5 )}{( 2 x + 4 ) ^{2}} : \frac{11}{2 ( x + 2 ) ^{2}}

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

Graph

Beliebte Beispiele

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y^'+3(tan(3x))y=7cos(3x)

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