derivative (x^4)/(1-x^3)

Lösung

ableitung von

\frac{x ^{4}}{1 - x ^{3}}

\frac{4 x ^{3} - x ^{6}}{( 1 - x ^{3} ) ^{2}}

Schritte zur Lösung

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

Vereinfache

\frac{4 x ^{3} ( 1 - x ^{3} ) - ( - 3 x ^{2} ) x ^{4}}{( 1 - x ^{3} ) ^{2}} : \frac{4 x ^{3} - x ^{6}}{( 1 - x ^{3} ) ^{2}}

= \frac{4 x ^{3} - x ^{6}}{( 1 - x ^{3} ) ^{2}}

a re a x^{2}, (- 2, 1)

\int \frac{x - 1}{x ( x + 1 )} d x

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

\int sin^{2} (X) d X

\frac{d}{d x} (6 cos (π x))