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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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d er i v a t i v e (x + 3)^{\frac{1}{2}}

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d er i v a t i v e tan^{2} (x - 1)

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d er i v a t i v e 4 \frac{t ^{5}}{5} - \frac{t ^{3}}{6}

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d er i v a t i v e \frac{10 x + x ^{2}}{2}