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

Lösung

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

- \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

Schritte zur Lösung

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

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

Vereinfache

\frac{( - 3 x ^{2} ) ( 1 + x ^{3} ) - 3 x ^{2} ( 1 - x ^{3} )}{( 1 + x ^{3} ) ^{2}} : - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

= - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}