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Beliebt Rechnen >

derivative of 1/(1+x^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (x^2-x+24)/(x^3+6x)

\int \frac{x ^{2} - x + 24}{x ^{3} + 6 x} d x

tangent y=x-3x^2,(3,-24)

t an g e n t y = x - 3 x^{2}, (3, - 24)

(\partial)/(\partial x)(3x^2y^4-2)

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

integral of (5x-7)e^{5x-7}

\int (5 x - 7) e^{5 x - 7} d x

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

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