Derivative of (y-siny)

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

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

   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:

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

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

   The result is: $1 - \cos{\left(y \right)}$

The answer is:

$$1 - \cos{\left(y \right)}$$