The problem states: Find dw/dt (a) using the appropriate chain rule and (b) by converting w to a function of t before differentiating.
w = xy x = s sin t, y = cos t
the solution in my solution manual goes like this:
a) using the chain rule they come up with: 2y cos t + x(-sin t) = 2y cos t - x sin t =
2(cos^2t - sin^2t) = 2 cos 2t
b) w = 2 sin t cos t = sin 2t, dw/dt = 2 cos 2t