[Solved] Should I include Order \"by column\" to index?

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Should I include Order \"by column\" to index?

I have a query

select * from cp where customer_Id = ? order by date_created desc limit 1

I like to optimize execution of this query bu creating index for customer_Id column.

Question: should my index contain date_created column also ?

How to optimize this SQL query?

The following recommendations will help you in your SQL tuning process.
You'll find 3 sections below:

  1. Description of the steps you can take to speed up the query.
  2. The optimal indexes for this query, which you can copy and create in your database.
  3. An automatically re-written query you can copy and execute in your database.
The optimization process and recommendations:
  1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
  2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
Optimal indexes for this query:
ALTER TABLE `cp` ADD INDEX `cp_idx_customer_id_date_created` (`customer_Id`,`date_created`);
ALTER TABLE `cp` ADD INDEX `cp_idx_date_created` (`date_created`);
The optimized query:
        cp.customer_Id = ? 
        cp.date_created DESC LIMIT 1

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* original question posted on StackOverflow here.