derivative (arctan(3x))^2

Lösung

ableitung von

(arctan (3 x))^{2}

\frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 arctan (3 x) \frac{3}{9 x ^{2} + 1} : \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

= \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

\frac{d}{d x} (15 sin (- π x) tan (\frac{2}{3} π x))

\int \frac{2 - v}{v ^{2} + 2 v - 3} d v

\frac{\partial}{\partial x} (x^{3} + a x y^{2})

x \to - \infty lim (\frac{4 arctan ( 8 x )}{e ^{x} + 2})

y^{^{'}} - 2 y = 3 e^{2 x}