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Beliebt Rechnen >

derivative of 1/(x(x+1))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (3t+3)^{2.2}

\int (3 t + 3)^{2.2} d t

derivative y=6x-11

d er i v a t i v e y = 6 x - 11

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

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

limit as x approaches 2 of 3.5+5.6

x \to 2 lim (3.5 + 5.6)

limit as x approaches 2-of (2-|x|)/(2+x)

x \to 2 - lim (\frac{2 - ∣ x ∣}{2 + x})