In[]:=
P1[ϕ_]:=2^-4((E^(I*(ϕ/2))+E^(-I*(ϕ/2)))(E^(I*(-(ϕ/2)))+E^(I*(ϕ/2))))^2;​​P2[ϕ_]:=2^-3(E^(I*(ϕ))-E^(-I*(ϕ)))(E^(I*(-ϕ))-E^(I*(ϕ)));​​P3[ϕ_]:=2^-4((E^(I*(ϕ/2))-E^(-I*(ϕ/2)))(E^(I*(-(ϕ/2)))-E^(I*(ϕ/2))))^2;​​​​L[ϕ_,m0_,m1_,m2_]:=((P02[ϕ])^m0)*((P11[ϕ])^m1)*((P20[ϕ])^m2)​​​​Refine[Simplify[P1[ϕ]+P2[ϕ]+P3[ϕ]],ϕ∈Reals]​​​​Refine[Simplify[L[ϕ,m0,m1,m2]],ϕ∈Reals]​​​​DL[ϕ_,m0_,m1_,m2_]:=D[Refine[Simplify[L[ϕ,m0,m1,m2]],ϕ∈Reals],ϕ]​​​​Simplify[DL[ϕ,m0,m1,m2]]
Out[]=
1
Out[]=
-4m0-3m1-4m2
2
m0

-2ϕ

4
(1+
ϕ

)

m2

2
(-2+
-ϕ

+
ϕ

)

m1
-
-2ϕ

2
(-1+
2ϕ

)

Out[]=
1
-1+
2ϕ


1-4m0-3m1-4m2
2
m0

-2ϕ

4
(1+
ϕ

)

m2

2
(-2+
-ϕ

+
ϕ

)

m1
-
-2ϕ

2
(-1+
2ϕ

)


2
(-1+
ϕ

)
m0+(1+
2ϕ

)m1+
2
(1+
ϕ

)
m2