derivative of x^3arctan(3x)

Lösung

\frac{d}{d x} (x^{3} arctan (3 x))

3 x^{2} arctan (3 x) + \frac{3 x ^{3}}{9 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (x^{3} arctan (3 x))

Wende die Produktregel an:

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

f = x^{3}, g = arctan (3 x)

= \frac{d}{d x} (x^{3}) arctan (3 x) + \frac{d}{d x} (arctan (3 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= 3 x^{2} arctan (3 x) + \frac{3}{9 x ^{2} + 1} x^{3}

Multipliziere Brüche:

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

= 3 x^{2} arctan (3 x) + \frac{3 x ^{3}}{9 x ^{2} + 1}

d er i v a t i v e 3 (sin (x))^{x}

a re a x^{2} - 4, x = - 4, x = 3

d er i v a t i v e 3 e

\frac{d}{d x} (ln (x^{2} - 14))

\int_{1}^{2} \frac{1}{x ^{3} + 4 x} d x