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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

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

Vereinfache

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

Graph

Beliebte Beispiele

tangent o2x2-3x+2

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\int 11 x d x

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

integral of 6/(6x-5)

\int \frac{6}{6 x - 5} d x