derivative of x^2arctan(4x)

Lösung

\frac{d}{d x} (x^{2} arctan (4 x))

2 x arctan (4 x) + \frac{4 x ^{2}}{16 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (x^{2} arctan (4 x))

Wende die Produktregel an:

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

f = x^{2}, g = arctan (4 x)

= \frac{d}{d x} (x^{2}) arctan (4 x) + \frac{d}{d x} (arctan (4 x)) x^{2}

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= 2 x arctan (4 x) + \frac{4}{16 x ^{2} + 1} x^{2}

Multipliziere Brüche:

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

= 2 x arctan (4 x) + \frac{4 x ^{2}}{16 x ^{2} + 1}

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