1. **State the problem:** Differentiate the function $f(x) = x - e^x$ with respect to $x$. 2. **Recall the differentiation rules:** - The derivative of $x$ with respect to $x$ is 1. - The derivative of $e^x$ with respect to $x$ is $e^x$. 3. **Apply the differentiation:** $$\frac{d}{dx}(x - e^x) = \frac{d}{dx}(x) - \frac{d}{dx}(e^x) = 1 - e^x$$ 4. **Final answer:** $$f'(x) = 1 - e^x$$ This means the slope of the function $x - e^x$ at any point $x$ is $1 - e^x$.