Nr 1

1.
nx^(n-1)
2.
sin(x)+xcos(x)
3.
(sos(x)^2+sin(x)^2)/cos(x)^2 = 1/cos(x)^2
4.
10x*1/5x^2 = 2/x
5.
x+cos(x^2/2)
6.
-1/4x^2
7.
(1-ln(x))/x^2

Nr. 3
	a)
p(a+b)
=pa1e1 + pa2e2 + pa3e3 + pb1e1 + pb2e2 + pb3e3
=p(a1e1 + a2e2 + a3e3) + p(b1e1 + b2e2 + b3e3)
=pa + pb
	b)
(a+b)*c
=(a1e1 + a2e2 + a3e3 + b1e1 + b2e2 + b3e3)*(c1e1 + c2e2 + c3e3)
da ei*ej nur 1 wenn i=j, sonst 0:
=a1c1 + a2c2 + a3b3 + b1c1 + b2c2 + b3c3
=ac + bc
	c)
a*b
=(a1e1 + a2e2 + a3e3) * (b1e1 + b2e2 + b3e3)
da ei*ej nur 1 wenn i=j, sonst 0:
=a1e1b1e1 + a2e2b2e2 + a3e3b3e3 
=a1b1 + a2b2 + a3b3
=b1a1 + b2a2 + b3a3
=a1e1b1e1 + a2e2b2e2 + a3e3b3e3 
da weggefallene Kombinationen keine nicht mehr enthaltenen Komponenten enthielten, kann Rckgeschlossen werden:
=(b1e1 + b2e2 + b3e3) * (a1e1 + a2b2 + a3b3)
=b*a 

