To find the derivative of Y with respect to x, we can use the chain rule.
Let u = 2x, then Y' = (cos(u))^2.
Now, differentiate with respect to u:
(d/du) cos(u) = -sin(u).
Now, multiply by the derivative of the inside function:
Y' = -2sin(2x)cos(2x)
Therefore, Y' = -2sin(2x)cos(2x).
To find the derivative of Y with respect to x, we can use the chain rule.
Let u = 2x, then Y' = (cos(u))^2.
Now, differentiate with respect to u:
(d/du) cos(u) = -sin(u).
Now, multiply by the derivative of the inside function:
Y' = -2sin(2x)cos(2x)
Therefore, Y' = -2sin(2x)cos(2x).