erweitern e^{(t-a)^2}u(t-a)

Lösung

erweitern

e^{(t - a)^{2}} u (t - a)

e^{t^{2} - 2 a t + a^{2}} t u - a e^{t^{2} - 2 a t + a^{2}} u

Schritte zur Lösung

e^{(t - a)^{2}} u (t - a)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = e^{(t - a)^{2}} u, b = t, c = a

= e^{(t - a)^{2}} u t - e^{(t - a)^{2}} u a

= e^{(t - a)^{2}} t u - a e^{(t - a)^{2}} u

Vereinfache

e^{(t - a)^{2}} t u - a e^{(t - a)^{2}} u : e^{t^{2} - 2 a t + a^{2}} t u - a e^{t^{2} - 2 a t + a^{2}} u

= e^{t^{2} - 2 a t + a^{2}} t u - a e^{t^{2} - 2 a t + a^{2}} u

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

e x p an d \frac{1}{cos ( x )}

e x p an d \frac{6 x ^{3} + 18 x ^{2} + 11 x + 2}{x ( 6 x ^{2} + 5 x + 1 )}

e x p an d - \frac{2}{4} (1 - s) (1 - t) + (- \frac{1}{4}) (1 + s) (1 - t)

e x p an d (sin (x) + cos (x)) (sec (x) + csc (x))