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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

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

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

Graph

Beliebte Beispiele

tangent y=0.03x^2+1

t an g e n t y = 0.03 x^{2} + 1

integral from 2 to 3 of 1/(4-3x)

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

integral of-3cos(x)

\int - 3 cos (x) d x

derivative of x^7(x-12^5)

\frac{d}{d x} (x^{7} (x - 12)^{5})

(dy)/(dx)= 1/(x-x^3)

\frac{d y}{d x} = \frac{1}{x - x ^{3}}