Derivative of y=5(1-cos(t))

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

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

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

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

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

   So, the result is: $5 \sin{\left(t \right)}$

The answer is:

$$5 \sin{\left(t \right)}$$