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Beliebt Rechnen >

derivative of (2x-6/(4-x))

Lösung

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (2 x - 6) = 2

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

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

Vereinfache

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

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

Graph

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