1. The problem is to find the derivative of the function $f(x) = x^3$ 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 $x^3$, we have: $$\frac{d}{dx} x^3 = 3 x^{3-1} = 3 x^2$$ 4. Therefore, the derivative of $x^3$ is $3x^2$. This means the slope of the curve $y = x^3$ at any point $x$ is $3x^2$.