we need to call convert_to_diff 2 time to obtain the right result in case of nested derivative.
display2d:false;
(%i140) pderivop(f,1)(pderivop(f,1)(x));
(%o140) pderivop(f,1)(pderivop(f,1)(x))
(%i141) convert_to_diff(%);
(%o141) 'at('diff(f(g11572),g11572,1),g11572 = pderivop(f,1)(x))
(%i142) convert_to_diff(%);
(%o142) 'at('diff(f(g11572),g11572,1),g11572 = 'diff(f(x),x,1))
Laurent.
Diff: