derivative x^{10}arctan(x)

Lösung

ableitung von

x^{10} arctan (x)

10 x^{9} arctan (x) + \frac{x ^{10}}{x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (x^{10} arctan (x))

Wende die Produktregel an:

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

f = x^{10}, g = arctan (x)

= \frac{d}{d x} (x^{10}) arctan (x) + \frac{d}{d x} (arctan (x)) x^{10}

\frac{d}{d x} (x^{10}) = 10 x^{9}

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

= 10 x^{9} arctan (x) + \frac{1}{x ^{2} + 1} x^{10}

\frac{1}{x ^{2} + 1} x^{10} = \frac{x ^{10}}{x ^{2} + 1}

= 10 x^{9} arctan (x) + \frac{x ^{10}}{x ^{2} + 1}

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