Derivative of 2sin(t)-1

1. Differentiate $2 \sin{\left(t \right)} - 1$ 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:

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

      So, the result is: $2 \cos{\left(t \right)}$

   2. The derivative of the constant $-1$ is zero.

   The result is: $2 \cos{\left(t \right)}$

The answer is:

$$2 \cos{\left(t \right)}$$