I tried using this code, but it does not work.
<?php print $node->field_slider_image['und'][0]['filename']; ?>
The full file object isn't necessarily loaded into the node object, you could try loading it manually and grabbing the filename/URL that way:
$file = file_load($node->field_slider_image['und'][0]['fid']);
// Filename
print $file->filename;
// URI e.g. public://image.jpg
print $file->uri;
// URL e.g. /sites/default/files/image.jpg
print file_create_url($file->uri);