Найти производную неявной функции e2xx+y2+2y=2

Ddxe2xx+2y+y2=ddx(2)
1) ddxuv=vdudx+udvdx, u=e2x, v=x+y2+2y:
e2xddxx+2y+y2+x+2y+y2ddxe2x=ddx(2)
ddxx+2ddxy+ddxy2e2x+ddxe2xx+2y+y2=ddx(2)
e2x2ddxy+ddxy2+1+ddxe2xx+2y+y2=ddx(2)
2) ddxy=dy(u)du*dudx, u=x, dduyu=y'(u):
e2x1+ddxy2+2ddxxy'x+ddxe2xx+2y+y2=ddx(2)
ddxe2xx+2y+y2+e2x1+ddxy2+1*2y'x=ddx(2)
3) ddxe2x=deudu*dudx, u=2x, ddueu=eu:
x+2y+y2*e2xddx2x+e2x1+ddxy2+2y'x=ddx(2)
2ddxxe2xx+2y+y2+e2x1+ddxy2+2y'x=ddx(2)
1*2e2xx+2y+y2+e2x1+ddxy2+2y'x=ddx(2)
4) ddxy2=du2du*dudx, u=y, dduu2=2u:
2e2xx+2y+y2+e2x1+2yddxy+2y'x=ddx(2)
5) ddxy=dy(u)du*dudx, u=x, dduyu=y'(u):
2e2xx+2y+y2+e2x1+ddxxy'x2y+2y'x=ddx(2)
2e2xx+2y+y2+e2x1+2y'x+1*2yy'x=ddx2
2e2xx+2y+y2+e2x1+2y'x+2yy'x=0
e2x+2e2xx+4e2xy+2e2xy2+2e2xy'x+2e2xyy'x=0
2e2xy'x+2e2xyy'x=-e2x-2e2xx-4e2xy-2e2xy2
2e2x+2e2xyy'x=-e2x-2e2xx-4e2xy-2e2xy2
y'x=-e2x-2e2xx-4e2xy-2e2xy22e2x+2e2xy