Problem with Jquery in Durpal 7 [closed]

Question

I am using Drupal 7 and bootstrap theme, I also have installed jquery update module,

Now I have created a js (jquery) file and saved it under js folder in bootstrap theme, I tried to call my js file in the info file using script[] = '...', the console then suggested that '$ is not a function', which means my js file was called before jquery was called.

Then I decided to call the my js file from template.php:

function bootstrap_preprocess_html(&$variables) {
  $options = array(
    'group' => JS_THEME,
  );
  drupal_add_js(drupal_get_path('theme', 'bootstrap'). 'js/product_pages.js', $options);
}

then the following line showed up in the console:

GET http://localhost/Brompton/sites/all/themes/bootstrapjs/product_pages.js?mpprnf 404 (Not Found) 

I am confused, how exactly can I get jquery work properly here?