derivative x^2arctan(3x)

Lösung

ableitung von

x^{2} arctan (3 x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = arctan (3 x)

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

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

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

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

Multipliziere Brüche:

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

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

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

d er i v a t i v e y = arccos (5 x)

\frac{d}{d x} (\frac{4}{x + 3})

\frac{d}{d x} (3 x - e^{x})

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