Here is some code that I think I found, but may have written, a long time ago.
First the Function. The key is the Nest, which takes care of the derivatives.
Clear[COV, DEQ, \[Psi], x, z, f, n] COV::usage = "COV[DEQ,\[Psi],x,z,f] changes the independent variable in a \ differential equation from x to z where x=f[z]. \[Psi] is the \ dependent variable or function we are solving for.";