Derivative of sin(x)-sqrt(3)cos(x)

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

   1. The derivative of sine is cosine:

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

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

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

         1. The derivative of cosine is negative sine:

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

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

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

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

2. Now simplify:

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

The answer is:

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