erweitern (D^2-5){e^{5x}cos(2x)}

Lösung

erweitern

(D^{2} - 5) {e^{5 x} cos (2 x)}

D^{2} e^{5 x} cos (2 x) - 5 e^{5 x} cos (2 x)

Schritte zur Lösung

(D^{2} - 5) {e^{5 x} cos (2 x)}

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = {e^{5 x} cos (2 x)}, b = D^{2}, c = 5

= {e^{5 x} cos (2 x)} D^{2} - {e^{5 x} cos (2 x)} \cdot 5

= D^{2} {e^{5 x} cos (2 x)} - 5 {e^{5 x} cos (2 x)}

Entferne die Klammern:

(a) = a

= D^{2} e^{5 x} cos (2 x) - 5 e^{5 x} cos (2 x)

e x p an d \frac{2 ( 1 + x )}{x ( x ^{2} + 4 )}

e x p an d - 2 (- C (sin (x)) - D (cos (x)))^{2}

e x p an d (4 x - \frac{1}{2})^{2}

e x p an d (1 - x^{2}) (L ((1 - x^{2})^{\frac{m ^{2}}{2}} - m^{2} x^{2} (1 - x^{2})^{\frac{m ^{2}}{2} - 1}))

s im pl i f y (2 - sin^{2} (x)) (cos^{2} (x))