derivative of xe^xcos(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

\int (5 x^{2} + 2 x^{3}) d x

\int (3 x + 5)^{6} d x

\frac{\partial}{\partial x} (5 cos (5 x))

\int t + 1 d t

im pl i c i t \frac{d y}{d x}, x^{(\frac{2}{3})} + y^{(\frac{2}{3})} = 10