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Beliebt Rechnen >

derivative of xarctan(x-1/2 ln(1+x^2))

Lösung

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

Lösung

arctan (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

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

= arctan (x)

Graph

Beliebte Beispiele

derivative of x/n

(\partial)/(\partial x)(-y/(4x^2+9y^2))

y^'=x^2y-x^2y^2,y(0)=17

derivative f(x)=sqrt(x)+5/(sqrt(x))

integral of sqrt(5-x)