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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative f(x)=2x^4-x^3+6x^2

d er i v a t i v e f (x) = 2 x^{4} - x^{3} + 6 x^{2}

tangent (x^2)/(x-2)

t an g e n t \frac{x ^{2}}{x - 2}

integral of tan(mx)sec^2(mx)

\int tan (m x) sec^{2} (m x) d x

limit as x approaches 3 of (3/x-1)/(x-3)

x \to 3 lim (\frac{\frac{3}{x} - 1}{x - 3})

integral from 1 to infinity of 2/(x^3)

\int_{1}^{\infty} \frac{2}{x ^{3}} d x