derivative of (x^3/(1-x^3))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (x + e^{z} + y)

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