Say that:
$$z = xy$$
So:
$${\partial z \over \partial x} = y$$
and
$${\partial z \over \partial y} = x$$
If we plot in 3D space the 2D surface corresponding to eq1, than take a point on that surface, the tangent with respect to the x axis is y, and the tangent corresponding to the y axis is x.
Do the total derivatives ($dz \over dx$ and $dz \over dy$) have a similar geometric interpretation?