I can answer one part of it for you

Sec=1/cos and, of course, tan=sin/cos. So that will give 1+tan(squared)

*u*=Sec(squared)

*u*
You should be able to google these rules.

When you differentiate using dy/dx=0 the e elements of the equation cancel each other out. As 1+tan(squared)x = Sec(squared)x, thats a simple substitution. Then you can simplify the equation and solve for Tan x.

Stick to the rules for working out circumferences of a circle and never forget the relationship of tan, sin and cos. Got me through my maths exams......but that was 20 years ago. I'm getting rusty in my old age.

Hope that helps