1. The problem is to find the derivative of the function $y = x^2$ with respect to $x$. 2. The formula for the derivative of a power function $y = x^n$ is given by: $$\frac{dy}{dx} = nx^{n-1}$$ where $n$ is a constant exponent. 3. Applying this rule to $y = x^2$, we identify $n = 2$. 4. Using the formula: $$\frac{dy}{dx} = 2x^{2-1} = 2x$$ 5. Therefore, the derivative of $x^2$ with respect to $x$ is $2x$. This means the slope of the curve $y = x^2$ at any point $x$ is $2x$.