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.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.