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Beliebt Rechnen >

derivative of (5+6x/(9-4x))

Lösung

\frac{d}{d x} (\frac{5 + 6 x}{9 - 4 x})

Lösung

\frac{74}{( 9 - 4 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 + 6 x}{9 - 4 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 + 6 x ) ( 9 - 4 x ) - \frac{d}{d x} ( 9 - 4 x ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}}

\frac{d}{d x} (5 + 6 x) = 6

\frac{d}{d x} (9 - 4 x) = - 4

= \frac{6 ( 9 - 4 x ) - ( - 4 ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}}

Vereinfache

\frac{6 ( 9 - 4 x ) - ( - 4 ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}} : \frac{74}{( 9 - 4 x ) ^{2}}

= \frac{74}{( 9 - 4 x ) ^{2}}

Graph

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