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Beliebt Rechnen >

derivative of x*arctan(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arctan (x)

= \frac{d x}{d x} arctan (x) + \frac{d}{d x} (arctan (x)) x

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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