derivative of e^{2x}cos(4x)

Lösung

\frac{d}{d x} (e^{2 x} cos (4 x))

2 e^{2 x} cos (4 x) - 4 e^{2 x} sin (4 x)

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} cos (4 x))

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= e^{2 x} \cdot 2 cos (4 x) + (- sin (4 x) \cdot 4) e^{2 x}

Vereinfache

= 2 e^{2 x} cos (4 x) - 4 e^{2 x} sin (4 x)

\int 6 x^{4} - 5 x^{3} + 5 x^{2} + C d x

x \to \infty lim (arctan (1 - x))

x \to 0 + lim (arctan (ln (x)))

\frac{d v}{d x} - \frac{1}{x} v = 8

d er i v a t i v e \frac{ln ( x )}{e ^{x}}