Answer:
dw/dt = -cos(t)(2sin(t) +1)
Explanation:
You want dw/dt for w = x² -y and x = cos(t), y = sin(t).
Derivative
w' = 2xx' -y' . . . . . . derivative with respect to t
w' = 2cos(t)(-sin(t)) -cos(t) . . . . . substitute given relations
dw/dt = -cos(t)(2sin(t) +1)