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Beliebt Rechnen >

derivative of 1/((x^2+x+1^3))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Graph

Beliebte Beispiele

fläche 2x+5,x^2+2x+1

a re a 2 x + 5, x^{2} + 2 x + 1

integral of 1/((x+6)(x+8))

\int \frac{1}{( x + 6 ) ( x + 8 )} d x

integral from 0 to 5 of 1/(x^{11/12)}

\int_{0}^{5} \frac{1}{x ^{\frac{11}{12}}} d x

integral of-1/(sqrt(x))

\int - \frac{1}{x} d x

derivative of ln(x^{13})

\frac{d}{d x} (ln (x^{13}))