What is the derivative of cos(2)?

The derivative of cos(2) is 0. The derivative of cos is -sin but, in this case, it does not matter once the chain rule and the constant rule are applied. It is also possible to simplify the expression first, which results in a constant of 0.999, and the derivative of any constant is always 0.

To find the derivative the long way, the chain rule must be used, which states that the derivative of the outside function, which is cos(x), gets multiplied by the derivative of the inside function, which in this case is 2. The derivative of 2 is 0, and the derivative of cos(x) is -sin(x), meaning the derivative here is equal to 0 times -sin(2) or 0.