How can I see that $\Bbb F_{p^2}(t)$ is a separable extension of $\Bbb F_p(t)$?

Question

I am given 2 examples to see that a imperfect field can have both separable and inseparable extensions.

I am told that $\Bbb F_{p^2}(t)$ is a separable extension of $\Bbb F_p(t)$, where $\Bbb F_p(t)$ is imperfect.

But how can I see that fact that $\Bbb F_{p^2}(t)$ is a seperable extension? May I please ask for a proof?

Answer 1

Hint: How do you get the field $\mathbb{F}_{p^2}$ from the field $\mathbb{F}_p$? The addition of the transcendent variable $t$ does not change things much.

Second hint: How does separability relate to minimal polynomials?