Производную функции f(x)=cos x/3 f(x)=sin2x f(x)=2/x f(x)=cos x/2

f(х) = (х * cos (2х)) = (х) * cos (2х) + х * (cos (2х)) = (х) * cos (2х) + х * (2х) * (sin (2х)) = 1 * cos (2х) + х * 2 * (-sin (2х)) = cos (2х) - 2хsin (2х).

f(х) = (х^3 * sin (2х)) = (х^3) * sin (2х) + х^3 * (sin (2х)) = (х^3) * sin (2х) + х^3 * (2х) * (sin (2х)) = 3х^2 * sin (2х) + х^3 * 2 * cos (2х) = 3х^2sin (2х) + 2х^3cos (2х).

f(х) = ((1 / 2) * х^2 (1 / 5) * х^5) = ((1 / 2) * х^2) ((1 / 5) * х^5) = (1 / 2) * 2 * х^(2 - 1) (1 / 5) * 5 * х^(5 - 1) = 1 * х^1 1 * х^4 = х х^4.

f(х) = (х * cos (2х)) = (х) * cos (2х) + х * (cos (2х)) = (х) * cos (2х) + х * (2х) * (sin (2х)) = 1 * cos (2х) + х * 2 * (-sin (2х)) = cos (2х) - 2хsin (2х).