1. **State the problem:** Find the derivative of the function $f(x) = \frac{x}{2} + x$ with respect to $x$. 2. **Recall the derivative rules:** - The derivative of $x$ with respect to $x$ is 1. - The derivative of a constant times a function is the constant times the derivative of the function. - The derivative of a sum is the sum of the derivatives. 3. **Apply the rules:** - Rewrite the function as $f(x) = \frac{1}{2}x + x$. - Derivative of $\frac{1}{2}x$ is $\frac{1}{2} \cdot 1 = \frac{1}{2}$. - Derivative of $x$ is 1. 4. **Add the derivatives:** $$\frac{d}{dx}\left(\frac{x}{2} + x\right) = \frac{1}{2} + 1 = \frac{3}{2}.$$