What is the derivative of x 2cosx?

For f(x) + g(x), the derivative d/dx[f(x) + g(x)] = f'(x) + g'(x). Essentially, this just means that since it's addition, you can take the derivative of each part.

d/dx(x - 2cosx) =

* d/dx is a way to indicate you're taking the derivative

d/dx(x) + d/dx(-2cosx)

* take the derivative of each part, distributing

(1) + (-2*-sinx)

* f(x) = x, f'(x) = 1 & g(x) = -2cosx, g'(x) = +2sinx

= 1 + 2sinx