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Beliebt Rechnen >

derivative of x^2arctan(8x)

Lösung

\frac{d}{d x} (x^{2} arctan (8 x))

Lösung

2 x arctan (8 x) + \frac{8 x ^{2}}{64 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (x^{2} arctan (8 x))

Wende die Produktregel an:

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

f = x^{2}, g = arctan (8 x)

= \frac{d}{d x} (x^{2}) arctan (8 x) + \frac{d}{d x} (arctan (8 x)) x^{2}

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

\frac{d}{d x} (arctan (8 x)) = \frac{8}{64 x ^{2} + 1}

= 2 x arctan (8 x) + \frac{8}{64 x ^{2} + 1} x^{2}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x arctan (8 x) + \frac{8 x ^{2}}{64 x ^{2} + 1}

Graph

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