Question: partial derivatives of thermodynamic functions

I am trying to solve a problem of liquid-liquid equilibrium based on the gibbs free energy equation:

DGdef := DG/RT = sum(n[i]*ln(phi[i]), i = 1 .. nc)+sum(sum(X[i, j]*n[i]*phi[j], j = i+1 .. nc), i = 1 .. nc)

DGdef1 := subs(n[i] = phi[i]*V/v[i], DGdef)

DG := eval(rhs(DGdef1), nc = 3)

DG1 := subs([phi[1] = phi1, phi[2] = phi2, phi[3] = phi3, v[1] = v1, v[2] = v2, v[3] = v3], DG)

Based on DG1 I need to derivate this expression with respect to phi1. However, phi1, phi2 and phi3 are interdependent because they are volume fractions. It means that phi1 is a function of phi2 & phi3. The same happens for phi2 and phi3.

If I simply use diff(DG1,phi1), Maple will solve it assuming no dependence among the fractions.

Someone know how to differentiate DG1 considering the interdependence among phi1, phi2 and phi3?

Thank you.