How can I find out what filesystem a particular directory is on

You can try:

df dirname

It should give the filesystem and mount point of the target of the symlink.

If you want to know the mount point and filesystem of the symlink itself:

df $(dirname /path/to/dirname)

^{(That's the command dirname and a dummy directory named "dirname", confusingly enough.)}

I know this provides a little more information than you requested. But you could make a simple C program using the realpath() library call. I have done this before to find out exactly where a specific file was. From there it should be a simple matter of determining the filesystem. A sample program would look like:

 /*
 * realpath - a program to find the real path
 */

 #include <limits.h>
 #include <stdlib.h>
 #include        <stdio.h>


 main(int argc, char **argv, char **envp)
 {
    void exit();
    char realx[10000];

    printf("\nORIGINAL PATH:\t%s\n",argv[1]);

    printf("Real PATH:\t%s\n",realpath(argv[1],realx));

    exit(0);

 }