Derivative of 1-cos(u)

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

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

   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:

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

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

   The result is: $\sin{\left(u \right)}$

The answer is:

$$\sin{\left(u \right)}$$