Derivatives of Trig functions

So my calculus book gives me

$\displaystyle (\sin x)'=\cos x$,

and

$\displaystyle (\sec x)'=\sec x \tan x$.

I have to differentiate

$\displaystyle \sin 2t$

and

$\displaystyle 3\sec^2 3t$.

So, for the first one, I would take $\displaystyle 2t$ to be $\displaystyle x$ and get

$\displaystyle \cos 2t$

but it says it should be

$\displaystyle 2\cos 2t$.

I don't understand how this works.

Also for the second one they get

$\displaystyle 18\sec^2 3t \tan 3t$,

and using the principle that I learned from the first one it makes sense except that the secant should not be squared.