erweitern e^xcos(x)(e^xcos(x)+e^xsin(x))

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

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

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

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

Vereinfache

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

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

e x p an d \frac{x}{( x - 2 ) ( x + 2 )}

e x p an d 3 cos (t) sin (t) - (2 t - 5)^{2} sin (t) + 3 t

f (x) = \frac{1}{( x - 1 ) ^{5}}

e x p an d - (x - 2) e^{2 x}

e x p an d ln (6 x^{9} y^{5})