Derivative of y=t-cost

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

   1. Apply the power rule: $t$ 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 cosine is negative sine:

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

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

   The result is: $\sin{\left(t \right)} + 1$

The answer is:

$$\sin{\left(t \right)} + 1$$