My textbook keeps saying it is
The best thing about life is you don't know what to expect
Your textbook is correct.
You can start with this page which shows how to get the derivative of arcsec
Then you just use the chain rule.
From the above link:
The chain rule says:
Now just substitute u = 1 / t and clean up.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.