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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Graph

Beliebte Beispiele

integral from 1 to 6 of 2/(x^3)

\int_{1}^{6} \frac{2}{x ^{3}} d x

t an g e n t 6 - 4 x^{2}

(dy)/(dx)-2/3 xy= 1/3 y^3

\frac{d y}{d x} - \frac{2}{3} x y = \frac{1}{3} y^{3}

integral of 4x^4(27+x^5)^{1/3}

\int 4 x^{4} (27 + x^{5})^{\frac{1}{3}} d x

integral of tsin(x)

\int t sin (x) d x