Find dz/dy at (1, ln 2, ln 3) if z(x, y) is defined by the equation xe^y+ye^z+2lnx-2-3ln2=0.

Differentiate both sides of xe^y+ye^z+2lnx-2-3ln2 = 0 with respect to y,

xe^y + e^z + ye^z ∂z/∂y = 0

Plug in (1, ln 2, ln 3),

2 + 3 + 3ln2 ∂z/∂y = 0

∂z/∂y = -5/(3ln2) <==Answer