Consider the following composition of the parametric curve: (x,y) = (sin 2t, cos t) with the quadric surface z=x^2+(y/3)^2[br][br]As the parameter t varies, it traces out the curve in the x,y plane. Above this point is corresponding point on the surface. [br][br]The composition of these functions z= sin^2(2t) +cos^2(t)/9 is the height of the point on the surface at time t.

Find [math]\frac{\partial z}{\partial x}, \frac{\partial z}{\partial y}[/math], dx/dt, dy/dt, and dz/dt. Can you express dz/dt as a combination of the others?