yz = ln(x+z), find partial derivatives

Question

Find partial derivatives of (del z)/(del x) and (del z)/(del y)

1. eq. yz = ln(x+z)

Answer 1

yz = ln(x + z);

y∂z/∂x = 1/(x+z)·(1 + ∂z/∂x); (x + z)y∂z/∂x = 1 + ∂z/∂x; ∂z/∂x = 1/(xy + zy - 1)

z + y∂z/∂y = (∂z/∂y)/(x + z); z(x + z) = (1 - xy - yz)∂z/∂y; ∂z/∂y = z(x + y)/(1 - xy - yz)