How Do You Differentiate y=sec^2(X) Where X is a Polynomial?

[Whitebread]

I need a quick check on my math. Derivative of composite function y=sec^2(X) where X is a polynomial.
Does it equal:
y'=(secXtanX)(secX)(X)(dy/dx)+(secX)(secXtanX)(dy/dx)(X)+(secX)(secX)(dy/dx)

I'm a little confused on applying the product rule and the chain rule to this function.

 

[Whitebread]

One more question. Compostie function y=csc(x) where X is a polynomial.
Does the first derivative of csc(X) equal:
y'=-csc(X)cot(X)(dy/dx)?

 

[StatusX]

I'm not sure what y is, but just apply the chain rule (ie, first the square, then the sec, then X).

 

[Hurkyl]

None of those can be right, since there is no y in your problem!

 

[Whitebread]

Ugh, stupid little things, I'll edit.

 

[Hurkyl]

y' = dy/dx.