Two Intermediates, One Input

A quantity $z$ is not written as one giant formula. It is built as a small computational graph with two intermediate nodes:

The inputs are $x$ and $y$. Notice that $x$ feeds both $u$ and $v$, so there is more than one route from the input to the output.

The graph is evaluated at

$x = 2, \qquad y = 3$

What is $\dfrac{\partial z}{\partial x}$ at that point? Give the exact value.