A derivative with respect to Euclidean distance?

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I have a function $y (x,z)$ from $\mathbb{R}_+^4$ to $\mathbb{R}$, where $x,z \in \mathbb{R}_+^2$.

I want to turn the following statement into math:
"the function $y$ is increasing as the Euclidean distance between $x$ and $z$ is increasing"

Can I write $\frac{ d y(x,z) }{\mathbb d c(x,z)}>0$, where $c(x,z)$ is the Euclidean distance between $x$ and $z$?