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Beliebt Rechnen >

derivative of (x^2/(10+x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{10 + x})

Lösung

\frac{20 x + x ^{2}}{( 10 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{10 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 10 + x ) - \frac{d}{d x} ( 10 + x ) x ^{2}}{( 10 + x ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (10 + x) = 1

= \frac{2 x ( 10 + x ) - 1 \cdot x ^{2}}{( 10 + x ) ^{2}}

Vereinfache

\frac{2 x ( 10 + x ) - 1 \cdot x ^{2}}{( 10 + x ) ^{2}} : \frac{20 x + x ^{2}}{( 10 + x ) ^{2}}

= \frac{20 x + x ^{2}}{( 10 + x ) ^{2}}

Graph

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