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Beliebt Rechnen >

derivative of (4x/(6x-1))

Lösung

\frac{d}{d x} (\frac{4 x}{6 x - 1})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x}{6 x - 1})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (6 x - 1) = 6

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

Vereinfache

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

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

Graph

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