Derivative of sqrt3*(sin(x))+cos(x)

1. Differentiate $\sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)}$ term by term:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

         $$\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$$

      So, the result is: $\sqrt{3} \cos{\left(x \right)}$

   2. The derivative of cosine is negative sine:

      $$\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$$

   The result is: $- \sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}$

2. Now simplify:

   $$2 \cos{\left(x + \frac{\pi}{6} \right)}$$

The answer is:

$$2 \cos{\left(x + \frac{\pi}{6} \right)}$$