Using the Chain Rule to solve? Also, find the derivative?

I am confused on what to do with the chain rule. I have a problem that goes a bit like this:

Assume that x, y, and z are all functions of time, t. Use the chain rule to find dz/dt, in terms of x, y, dx/dt and dy/dt if z= sin(x y).

How do I use the chain rule to solve this? Please help me solve and tell me the steps you used to get to it. I have this so far: dz/dt = cosx dy/dt y dx/dt, but I'm pretty sure that's wrong.

Also, I'm confused on how to find the derivative for this one. I get kind of confused when there are squares along with it:

d/dx [sin(x^2)+cos^2(x)].

Any help GREATLY appreciated! Thanks so much.