In[]:=
<<Notation`​​Symbolize
r
2
​​ClearAll[r,θ,ur,f,n];​​ur[r_,θ_]:=
n
r
2
n+1
r
Cos[nθ];​​f[r_,θ_]:=
n
r
2
n+1
r
Cos[nθ];​​
∂
r
ur[r,θ]​​
∂
r
f[r,θ]
Out[]=
(-1-n)
-2-n
r
n
r
2
Cos[nθ]
Out[]=
-(1+n)
-2-n
r
n
r
2
Cos[nθ]
′
HoldForm

-1-n
r
n
r
2
Cos[nθ]