Mail sent from Apple Mail is not show in Gmail's Sent folder
Ensure that in your mail settings you have:

IMAP Path Prefix: [Gmail]


Under the Mailbox Behaviors tab in Accounts settings you have checked:

√ Store sent messages on the server
Delete sent messages when: Never


In the Sidebar of Mail, there should be grey subheadings for your accounts. Under the Grey subheading for your gmail account, you will find folders with titles of your gmail tags (e.g. Important, Starred, etc.) If you see one there called Sent Mail, select it, and select this menu item: Mailbox > Use This Mailbox For > Sent.