In[120]:= p[a_] := Log[q[a]]
In[132]:= u = D[p[a], {a, 4}]
Out[132]= -((6 Derivative[1][q][a]^4)/q[a]^4) + (
12 Derivative[1][q][a]^2 (q^\[Prime]\[Prime])[a])/q[a]^3 - (
3 (q^\[Prime]\[Prime])[a]^2)/q[a]^2 - (4 Derivative[1][q][a]
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[a])/q[a]^2 +
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[a]/q[a]
In[133]:= Together[u]
Out[133]= (-6 Derivative[1][q][a]^4 +
12 q[a] Derivative[1][q][a]^2 (q^\[Prime]\[Prime])[a] -
3 q[a]^2 (q^\[Prime]\[Prime])[a]^2 - 4 q[a]^2 Derivative[1][q][a]
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[a] + q[a]^3
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[a])/q[a]^4
