erweitern (e^tcos(t)-e^tsin(t))*(2e^tcos(t))

Lösung

erweitern

(e^{t} cos (t) - e^{t} sin (t)) \cdot (2 e^{t} cos (t))

2 e^{2 t} cos^{2} (t) - 2 e^{2 t} sin (t) cos (t)

Schritte zur Lösung

(e^{t} cos (t) - e^{t} sin (t)) (2 e^{t} cos (t))

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (2 e^{t} cos (t)), b = e^{t} cos (t), c = e^{t} sin (t)

= (2 e^{t} cos (t)) e^{t} cos (t) - (2 e^{t} cos (t)) e^{t} sin (t)

= e^{t} cos (t) (2 e^{t} cos (t)) - e^{t} sin (t) (2 e^{t} cos (t))

Vereinfache

e^{t} cos (t) (2 e^{t} cos (t)) - e^{t} sin (t) (2 e^{t} cos (t)) : 2 e^{2 t} cos^{2} (t) - 2 e^{2 t} sin (t) cos (t)

= 2 e^{2 t} cos^{2} (t) - 2 e^{2 t} sin (t) cos (t)

e x p an d \frac{( 5 x - 22 ) ( x - 1 )}{x + 5}

\frac{\partial}{\partial x} ((y) (x^{3} y - x - 5 y - 10))

e x p an d \frac{( 4 - 3 i ) ^{6}}{6}

e x p an d (2 x^{3} + \frac{b}{x})^{8}

e x p an d (cos (x) + sin (y))^{2}