fucking derivatives

Just double checking because while learning derivatives the exciting yet doublecrossing chain rule gets the best of me.

y=[tan(x^2+1)]^2

I got y'=(4x)(tan(x^2+1))(sec^2(x^2+1))

Am I correct?

Greetings, good sir.

I have heard you enjoy differentials.  Accordingly, I have placed a function inside of another function, thus allowing you to derive while you derive.