Was Tamil derived from Sanskrit ?

Tamil wasn’t derived from Sanskrit.

Both the languages belong to completely different language families.

Tamil belongs to Dravidian language family:

The above picture shows the regions where Dravidian languages are spoken.

Sanskrit is a Indo-European language. It belongs to the Indo-Iranian subgroup.

Indo-European languages:

Let’s see some examples from linguistic point of view to understand the basic difference between the language families:

Indo European :

English : who is your son ?

Sanskrit: Kaha tava sūnu?

Lithuanian: Kas tavo sūnus?

Russian : kto tvoy syn ?

Bulgarian : koĭ e tvoyat sin?

Czech: kdo je tvůj syn ?

Slovenian: kdo je tvoj sin?

English: That is you.

Sanskrit: tat tvam asi

Lithuanian: tas tu esi

Latvian : Tas esi tu