Derivative of 14*sqrt(3)*cos(x)+14*sin(x)

1. Differentiate $14 \sin{\left(x \right)} + 14 \sqrt{3} \cos{\left(x \right)}$ 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 cosine is negative sine:

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

      So, the result is: $- 14 \sqrt{3} \sin{\left(x \right)}$

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

      1. The derivative of sine is cosine:

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

      So, the result is: $14 \cos{\left(x \right)}$

   The result is: $- 14 \sqrt{3} \sin{\left(x \right)} + 14 \cos{\left(x \right)}$

2. Now simplify:

   $$28 \cos{\left(x + \frac{\pi}{3} \right)}$$

The answer is:

$$28 \cos{\left(x + \frac{\pi}{3} \right)}$$