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Beliebt Rechnen >

derivative x/(5x+2)

Lösung

ableitung von

\frac{x}{5 x + 2}

Lösung

\frac{2}{( 5 x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{5 x + 2})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (5 x + 2) = 5

= \frac{1 \cdot ( 5 x + 2 ) - 5 x}{( 5 x + 2 ) ^{2}}

Vereinfache

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

Graph

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