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

Lösung

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

\frac{16 x ^{3} - x ^{6}}{( 4 - x ^{3} ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{4 x ^{3} ( 4 - x ^{3} ) - ( - 3 x ^{2} ) x ^{4}}{( 4 - x ^{3} ) ^{2}} : \frac{16 x ^{3} - x ^{6}}{( 4 - x ^{3} ) ^{2}}

= \frac{16 x ^{3} - x ^{6}}{( 4 - x ^{3} ) ^{2}}

d er i v a t i v e cos (x) - 4 tan (x)

\frac{\partial}{\partial x} (8 - x^{2} - 3 y^{2})

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d er i v a t i v e \frac{6}{x ^{3}} - \frac{6}{x ^{2}} - \frac{1}{x} + 350

\frac{d}{d x} (x^{3} + 5 x)