Derivative of y=e-sint

1. Differentiate $e - \sin{\left(t \right)}$ term by term:

   1. The derivative of the constant $e$ is zero.

   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:

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

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

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

The answer is:

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