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You may find the shell $OLDPWD shell variable useful (defined by POSIX). For example, you could define a shell function overriding the original cd command:
cd() { command cd "$@" && printf '%s -> %s\n' "${OLDPWD}" "${PWD}"; }
Excerpt from the Unix man page you should read:
If, during the execution of the above steps, the PWD environment ...
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