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Beliebt Rechnen >

derivative of (x^3-2x+4/(x^3))

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of x(5x-3)^2

integral of e^{3x}+1/x

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y^'+3y=2e^{-3t}

derivative f(x)=((sqrt(x)-2))/((2x^2+3))