Derivative of y(x)=sinx-e^x-x

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

   1. The derivative of sine is cosine:

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

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

      1. The derivative of $e^{x}$ is itself.

      So, the result is: $- e^{x}$

   3. 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: $-1$

   The result is: $- e^{x} + \cos{\left(x \right)} - 1$

The answer is:

$$- e^{x} + \cos{\left(x \right)} - 1$$