I'm a little confused with this question:

If $\displaystyle y = sec^s (x^2)$, then $\displaystyle \frac {dy}{dx} = $

- (A) $\displaystyle 2xsec(x^2)tan(x^2)$
- (B) $\displaystyle 4xsec(x^2)tan(x^2)$
- (C) $\displaystyle sec^2(x^2)tan(x^2) $
- (D) $\displaystyle 4xsec^2(x^2)$
- (E) $\displaystyle 4xsec^2(x^2)tan(x^2)$

See, what I'm not sure about is whether $\displaystyle sec^2(x^2)$ can be written as $\displaystyle (sec x)^2 $ or $\displaystyle (sec x^2)^2$

In the first way, I'd get:

$\displaystyle

\frac {d}{dx}[(sec x)^2] = 2secxtanx$

which isn't a choice, but choice (A) is similar...

And if I use the second way:

$\displaystyle

\frac {d}{dx}[(sec x^2)^2] = 2(sec x^2)(sec x^2tan^2)

$

Which isn't in the choices, either. >_<

Help ? Please & Thank you =)