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Beliebt Rechnen >

derivative arctan(x/2)

Lösung

ableitung von

arctan (\frac{x}{2})

Lösung

\frac{2}{x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{x}{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{2}{x ^{2} + 4}

Graph

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