Derivative of 2cosx-3

1. Differentiate $2 \cos{\left(x \right)} - 3$ 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: $- 2 \sin{\left(x \right)}$

   2. The derivative of the constant $-3$ is zero.

   The result is: $- 2 \sin{\left(x \right)}$

The answer is:

$$- 2 \sin{\left(x \right)}$$