This question may not belong here but it is a simple derivative question including vectors.

$\displaystyle \vec{r} = a\sin(\omega t) \hat{x} + b\cos(\omega t) \hat{y}; \:\:\: \hat{x}, \hat{y}$ are unit vectors

$\displaystyle (\vec{r})^\prime = ?$

I have a couple questions:

1) is the derivative of sin(wt), cos(wt), or do I do something extra with the angle in the parenthesis?

2) is the unit vector x considered a function? and if so what is it's derivative? I would assume $\displaystyle \hat{x}^\prime = 1$