derivative of x^2e^xcos(2x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

\frac{d}{d x} (- 6 cot (x) csc (x))

\frac{\partial}{\partial x} ((1 + 2 x^{2}) (x - x^{2}))

s l o p e in t erce pt (7.2) (2.8)

\int_{- 6}^{6} 58

x \to 4 lim (\frac{∣ x ∣}{x})