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Beliebt Rechnen >

derivative of x/(5x+8)

Lösung

\frac{d}{d x} (\frac{x}{5 x + 8})

Lösung

\frac{8}{( 5 x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{5 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( 5 x + 8 ) - \frac{d}{d x} ( 5 x + 8 ) x}{( 5 x + 8 ) ^{2}}

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

\frac{d}{d x} (5 x + 8) = 5

= \frac{1 \cdot ( 5 x + 8 ) - 5 x}{( 5 x + 8 ) ^{2}}

Vereinfache

= \frac{8}{( 5 x + 8 ) ^{2}}

Graph

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