# Thread: Partial Derivatives...

1. ## Partial Derivatives...

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?

2. Originally Posted by abradfo1
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.

$z_y = \cos(x-y) + y\sin(x-y)$

$z_x = -y\sin(x-y)$

Your different answers may actually be the same. For instance, don't forget little things like that $\cos(x-y) = \cos(y-x)$, and $\sin(x-y) = -\sin(y-x)$. This could cause your answers to look different but still might all be correct.