Well the chain rule is f(g(x))' = f'(g(x)) × g'(x)
The derivative of the cos function is the negative sin function. So the first part is -Asin(wt + sigma)
Then take the derivative of the function inside the parenthesis to get w since the derivative of wt with respect to the is w, and the derivative of sigma is 0 assuming it is a constant.
Therefore the derivative of the entire function is -Awsin(wt + sigma).
This may be wrong since I am just learning about derivatives, but it is what I would do.
