I'm having trouble with the concept. I need to find the partials dz/dy and dz/dx when z=ycos(x-y) and keep coming up with different answers... Can anyone help?
With partial derivatives, you just treat all the variable as constants except the one you're differentiating with respect to.
$\displaystyle z_y = \cos(x-y) + y\sin(x-y)$
$\displaystyle z_x = -y\sin(x-y)$
Your different answers may actually be the same. For instance, don't forget little things like that $\displaystyle \cos(x-y) = \cos(y-x)$, and $\displaystyle \sin(x-y) = -\sin(y-x)$. This could cause your answers to look different but still might all be correct.