1. The problem is to find the derivative of the function $f(x) = x^2$. 2. The formula for the derivative of a power function $f(x) = x^n$ is given by the power rule: $$\frac{d}{dx} x^n = n x^{n-1}$$ 3. Applying the power rule here with $n=2$, we get: $$\frac{d}{dx} x^2 = 2 x^{2-1} = 2x$$ 4. This means the slope of the function $x^2$ at any point $x$ is $2x$. 5. Therefore, the derivative of $x^2$ is $2x$.