Derivative Curve 41742A

1. **State the problem:** We are given the curve $$y = x^3 - 6x^2 + 9x + 4$$ and need to find its derivative $$\frac{dy}{dx}$$. 2. **Recall the derivative rules:** - The derivative of $$x^n$$ is $$nx^{n-1}$$. - The derivative of a constant is 0. - The derivative of a sum is the sum of the derivatives. 3. **Apply the derivative to each term:** - Derivative of $$x^3$$ is $$3x^2$$. - Derivative of $$-6x^2$$ is $$-6 \times 2x = -12x$$. - Derivative of $$9x$$ is $$9$$. - Derivative of $$4$$ is $$0$$. 4. **Combine the results:** $$\frac{dy}{dx} = 3x^2 - 12x + 9$$. 5. **Final answer:** $$\boxed{\frac{dy}{dx} = 3x^2 - 12x + 9}$$.