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).