derivative of 1/(x^3+2)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 2 lim (x^{3} - 2 x^{2} + x - 3)

d er i v a t i v e (2 - 3 x^{2})^{4} (x^{7} + 3)^{3}

d er i v a t i v e f (x) = \frac{x}{4}

\frac{d}{d x} (2 + 5 x)

n = 2 \sum \infty n^{2} - n