1. **State the problem:** Differentiate the function $$y = 2\cos x + \sin x$$ with respect to $$x$$. 2. **Recall differentiation rules:** - The derivative of $$\cos x$$ is $$-\sin x$$. - The derivative of $$\sin x$$ is $$\cos x$$. - The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. 3. **Apply the derivative:** $$\frac{dy}{dx} = 2 \cdot \frac{d}{dx}(\cos x) + \frac{d}{dx}(\sin x)$$ 4. **Substitute derivatives:** $$\frac{dy}{dx} = 2 \cdot (-\sin x) + \cos x$$ 5. **Simplify:** $$\frac{dy}{dx} = -2\sin x + \cos x$$ **Final answer:** $$\boxed{\frac{dy}{dx} = -2\sin x + \cos x}$$