Derive $x$ when given $g,g^x$ and $g^{(1/x)}$? If an adversary has access to the generator g of a group G and is given access to $g^{x}$ and $g^{(1/x)}$, will it make it any easier to derive the value of $x$ compared to when he had access to only $g$ and $g^{x}$?

EDIT: My question is different from “Can we reduce Diffie-Hellman problem to “Discrete-log inversion” problem?” as in this case the adversary has the values and does not need an oracle to derive it
Any group where you can derive $x$ from $g, g^x, g^{1/x}$ would also have the Discrete Log problem be equivalent to the (computational) Diffie-Hellman problem.  Since this is not known to be true in general, we don't know of any general method for deriving $x$ from those values.

This equivalence is quite simple to demonstrate; if it based on the fact that solving the cDH program allows us to compute $g^{1/x}$ given $g, g^x$.  So, if we assume we can recover $x$ from $g, g^x, g^{1/x}$, then we can solve the Discrete Log problem (given $g, g^x$) by first recovering $g^{1/x}$ (using our cDH Oracle), and then given $g, g^x, g^{1/x}$, recover $x$