1. The problem is to find the derivative of the function $x^2$ with respect to $x$. 2. The formula for the derivative of a power function $x^n$ is given by the power rule: $$\frac{d}{dx} x^n = n x^{n-1}$$ 3. Applying the power rule to $x^2$, we have: $$\frac{d}{dx} x^2 = 2 x^{2-1} = 2x$$ 4. Therefore, the derivative of $x^2$ with respect to $x$ is $2x$. This means that the slope of the curve $y = x^2$ at any point $x$ is $2x$.