derivative of xarctan(2x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = arctan (2 x)

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

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

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

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

Vereinfache

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

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

x \to 0 - lim (x csc (x))

\frac{d ^{2}}{d x ^{2}} (cos (- 2 x))

\frac{d}{d x} (cos (x^{2} + π))

d er i v a t i v e g (t) = 2^{t}

t a y l or x^{2} e^{x - 1}, at 1