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Beliebt Rechnen >

derivative of 4/(x^2+1)

Lösung

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

Lösung

- \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

4 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x) : - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Graph

Beliebte Beispiele

limit as x approaches 0 of 1/(2x)-1/(e^{2x)-1}

x \to 0 lim (\frac{1}{2 x} - \frac{1}{e ^{2 x} - 1})

(\partial)/(\partial x)(x^2)

\frac{\partial}{\partial x} (x^{2})

derivative sqrt(7x)-sqrt(2x)

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d er i v a t i v e y = 20 x^{3} (x^{4} + 5)^{4}

integral from 0 to 4 of (x-4)^2

\int_{0}^{4} (x - 4)^{2} d x