(\partial)/(\partial x)(xe^{2x}cos(3x))

Lösung

\frac{\partial}{\partial x} (x e^{2 x} cos (3 x))

e^{2 x} cos (3 x) + x (2 e^{2 x} cos (3 x) - 3 e^{2 x} sin (3 x))

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{2 x} cos (3 x))

Wende die Produktregel an:

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

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

= \frac{\partial}{\partial x} (x) e^{2 x} cos (3 x) + \frac{\partial}{\partial x} (e^{2 x} cos (3 x)) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{2 x} cos (3 x)) = 2 e^{2 x} cos (3 x) - 3 e^{2 x} sin (3 x)

= 1 \cdot e^{2 x} cos (3 x) + (2 e^{2 x} cos (3 x) - 3 e^{2 x} sin (3 x)) x

Vereinfache

= e^{2 x} cos (3 x) + x (2 e^{2 x} cos (3 x) - 3 e^{2 x} sin (3 x))

\int e^{x} sin (e^{x}) d x

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

x \to - 1 lim (\frac{2 x + 1}{x - 2})

t an g e n t x^{2} + 3 x, at x = 0

\int - 5 ln (x^{2} - 1) d x