1. The problem asks to find the partial derivative of the function $u = x + y + z$ with respect to $x$. 2. The formula for the partial derivative of a function $u$ with respect to a variable $x$ is written as $\frac{\partial u}{\partial x}$. 3. Since $u = x + y + z$, and $y$ and $z$ are treated as constants when differentiating with respect to $x$, the derivative of $x$ with respect to $x$ is 1, and the derivatives of $y$ and $z$ with respect to $x$ are 0. 4. Therefore, $$\frac{\partial u}{\partial x} = \frac{\partial}{\partial x}(x) + \frac{\partial}{\partial x}(y) + \frac{\partial}{\partial x}(z) = 1 + 0 + 0 = 1.$$