The definition of arc length of a parametric function is given by $\int|r'(t)|dt=\int\sqrt{[x'(t)]^2+[y'(t)]^2+[z'(t)]^2} dt$
So I guess what I'm asking is how do I use a function like $z=\cos(x)+\sin(y)$ with this definition? I am aware that $z(x,y)$ is a surface, but is it possible to find the distance between two points through the surface using this definition? If not, then how do I go about doing so?
Example:
z=\cos(x)+\sin(y)"> If I were an ant along this surface, how would I find the distance needed to travel between one of the peaks and wells in this graph?