Derivative of (56*cos(x)+28*sqrt(3)*x-28*sqrt(3)*pi)/(3+22)

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

   1. Differentiate $28 \sqrt{3} x + 56 \cos{\left(x \right)} - 28 \sqrt{3} \pi$ 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: $- 56 \sin{\left(x \right)}$

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

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $28 \sqrt{3}$

      3. The derivative of the constant $- 28 \sqrt{3} \pi$ is zero.

      The result is: $- 56 \sin{\left(x \right)} + 28 \sqrt{3}$

   So, the result is: $\frac{- 56 \sin{\left(x \right)} + 28 \sqrt{3}}{3 + 22}$

2. Now simplify:

   $$- \frac{56 \sin{\left(x \right)}}{25} + \frac{28 \sqrt{3}}{25}$$

The answer is:

$$- \frac{56 \sin{\left(x \right)}}{25} + \frac{28 \sqrt{3}}{25}$$