Question

given sin(x+y)+sin(x+z)+sin(y+z)=-1, which defines z implicitly in terms of x and y, find the directional derivative of z in the direction -i+2j at the point P(pi,pi/2),with z=pi/4 at P

Answer 1

im not sure if i did it right but i found that,
dz/dx = -1/2
dz/dy = -1/2
at the point P