Final answer:
The derivative of y = sin(x)cos(x) is -1/2 at x = π/3.
Step-by-step explanation:
To find dy/dx at x = π/3, we first need to find the derivative of y with respect to x.
Using the product rule, we differentiate sin(x)cos(x) as follows:
dy/dx = cos(x)cos(x) - sin(x)sin(x)
dy/dx = cos^2(x) - sin^2(x)
Now, substitute x = π/3 into the expression for dy/dx:
dy/dx = cos^2(π/3) - sin^2(π/3)
dy/dx = (1/4) - (3/4)
dy/dx = -1/2