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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(\partial)/(\partial y)(2y+1)

\frac{\partial}{\partial y} (2 y + 1)

derivative (t+1)^3sqrt(t^2+84)

d er i v a t i v e (t + 1)^{3} t^{2} + 84

derivative x^2arctan(2x)

d er i v a t i v e x^{2} arctan (2 x)

taylor e^{x-1},1

t a y l or e^{x - 1}, 1

derivative f(x)=(4x^2)/((x^2+x)^3)

d er i v a t i v e f (x) = \frac{4 x ^{2}}{( x ^{2} + x ) ^{3}}