Найдите абсциссы точек графика функции y=1/2cos2x-x в которых касательные к этому графику параллельны оси абсцисс или совпадают с ней

Possible derivation:

d/dx (y) = d/dx (1/2 cos (2 x) - x)

The derivative of y is zero:

0 = d/dx (-x+1/2 cos (2 x))

Differentiate the sum term by term and factor out constants:

0 = (d/dx (cos (2 x))) / 2-d/dx (x)

The derivative of x is 1:

0 = 1/2 (d/dx (cos (2 x))) - 1

Using the chain rule, d/dx (cos (2 x)) = (dcos (u)) / (du) (du) / (dx), where u = 2 x and (d) / (du) (cos (u)) = - sin (u) :

0 = - 1+1/2-d/dx (2 x) sin (2 x)

Factor out constants:

0 = - 1-1/2 sin (2 x) 2 d/dx (x)

Simplify the expression:

0 = - 1 - (d/dx (x)) sin (2 x)

The derivative of x is 1:

Answer: |

| 0 = - 1-1 sin (2 x)