дальше находим:
d^(2)z/dy^2=(-3e^(x-3y)*sin(x+3y)+3cos(x+3y)*e^(x-3y))' по y=
=(-3e^(x-3y)*sin(x+3y))'+(3*cos(x+3y)*e^(x-3y))'=
=(-3e^(x-3y)*(sin(x+3y))'+sin(x+3y)*(3e^(x-3y))')+(3cos(x+3y)*(e^(x-3y))'+e^(x-3y)*(3cos(x+3y))')=
=(-3e^(x-3y)*cos(x+3y)*(x+3y)'+sin(x+3y)*(x-3y)'*3e^(x-3y))+(3cos(x+3y)*(x-3y)'*e^(x-3y)+e^(x-3y)*(-3sin(x+3y)*(x+3y)')=
=(-3e^(x-3y)*cos(x+3y)*3+sin(x+3y)*(-3)*3e^(x-3y))+(3cos(x+3y)*(-3)*e^(x-3y)+e^(x-3y)*(-3sin(x+3y)*3)=
=(-9e^(x-3y)*cos(x+3y)-9e^(x-3y)*sin(x+3y))+(-9e^(x-3y)*cos(x+3y)-9e^(x-3y)*sin(x+3y))=
=-9e^(x-3y)*cos(x+3y)-9e^(x-3y)sin(x+3y)-9e^(x-3y)*cos(x+3y)-9e^(x-3y)*sin(x+3y)=
=-18e^(x-3y)*cos(x+3y)-18*e^(x-3y)*sin(x+3y)


верно?