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Beliebt Rechnen >

derivative of 1/(x^3+1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(dy)/(dx)=xy+4x+5y+20

\frac{d y}{d x} = x y + 4 x + 5 y + 20

integral from-2 to 3 of (45)/(x^4)

\int_{- 2}^{3} \frac{45}{x ^{4}} d x

(dy)/(dx)=(x+y)/(x+y+2)

\frac{d y}{d x} = \frac{x + y}{x + y + 2}

integral of (x+5)/(x^2(x-2))

\int \frac{x + 5}{x ^{2} ( x - 2 )} d x

limit as x approaches 0 of ln(1)

x \to 0 lim (ln (1))