I need help finding the derivative of f(x)=secx^2 using the double angle formula. I know that the answer is 2xsec(x^2)tan(x^2) but I don't understand how they got the answer.

Thank you for the opportunity to help you with your question!

identities

Notice how a "co-(something)"
trig ratio is always the reciprocal of some "non-co" ratio.
You can use this fact to help you keep straight that cosecant goes with
sine and secant goes with cosine.

The above, because they involve squaring
and the number 1, are the "Pythagorean" identities. You can
see this clearly if you consider the unit circle, where sin(t)
= y, cos(t)
= x, and the hypotenuse is 1.