My parents claim me, and they live in DE. I am in college in Tenn., have a a part time job and all $ from my part time job was earned here. Do I pay DE state taxes?

[KathrynG3]

Yes. Even though the income was earned in Tennessee, where there is no income tax requirement, the permanent resident state is allowed to tax all income earned with a credit allowed only for any amount of tax paid to another state. 

See 2019 Delaware Form 200-01 Instructions, page 5 stating that the income must begin with the Federal Adjusted Gross Income and page 6 about line 10, Other State Tax Credit.

@mattmoshe

[Hal_Al]

Yes. A  student, attending school out-of-state, is considered a resident of the state where his parents live, if he is their dependent.