1. **State the problem:** Find the derivative of the function $$y = \frac{x^3}{4} - 3x$$. 2. **Recall the derivative rules:** - The derivative of $$x^n$$ is $$nx^{n-1}$$. - The derivative of a constant times a function is the constant times the derivative of the function. - The derivative of $$x$$ is 1. 3. **Apply the power rule to each term:** - For $$\frac{x^3}{4}$$, rewrite as $$\frac{1}{4}x^3$$. - Derivative is $$\frac{1}{4} \times 3x^{3-1} = \frac{3}{4}x^2$$. - For $$-3x$$, derivative is $$-3 \times 1 = -3$$. 4. **Combine the derivatives:** $$\frac{dy}{dx} = \frac{3}{4}x^2 - 3$$. 5. **Final answer:** $$\boxed{\frac{dy}{dx} = \frac{3}{4}x^2 - 3}$$