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Beliebt Rechnen >

derivative of (x^2/(1+x^3))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{3}})

Lösung

\frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + x ^{3} ) - \frac{d}{d x} ( 1 + x ^{3} ) x ^{2}}{( 1 + x ^{3} ) ^{2}}

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

\frac{d}{d x} (1 + x^{3}) = 3 x^{2}

= \frac{2 x ( 1 + x ^{3} ) - 3 x ^{2} x ^{2}}{( 1 + x ^{3} ) ^{2}}

Vereinfache

\frac{2 x ( 1 + x ^{3} ) - 3 x ^{2} x ^{2}}{( 1 + x ^{3} ) ^{2}} : \frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

= \frac{2 x - x ^{4}}{( 1 + x ^{3} ) ^{2}}

Graph

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