I took you down the wrong rabbit-hole and its ENTIRELY my fault, sorry about that.
We do have functions in C+±land whose derivatives are entirely defined by tracing, but this is not such a function.
inverse's derivate is speficied in derivatives.yaml here: https://github.com/pytorch/pytorch/blob/ef487d4f1d7b167dc28976b90e3a728006f37a55/tools/autograd/derivatives.yaml#L396-L397 75