Specify the function for which the function F (x) = 2-cosx is antiderivative.

Using basic differentiation formulas and differentiation rules:

(x ^ n) ‘= n * x ^ (n-1).

(e ^ x) ‘= e ^ x.

(cos (x) ‘= -sin (x).

(c * u) ’= c * u’, where c is const.

(u ± v) ‘= u’ ± v ‘.

(uv) ‘= u’v + uv’.

y = f (g (x)), y ‘= f’u (u) * g’x (x), where u = g (x).

Thus, the derivative of our given function will look like this:

f (x) ‘= (x * cos (x))’ = (x) ‘* cos (x) + x * (cos (x))’ = 1 * cos (x) + x * (-sin (x )) = cos (x) – x * sin (x).

Answer: The derivative of our given function will be equal to f (x) ‘= cos (x) – x * sin (x).