curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule).

x=4tan(t) hence dx/dt = 4 sec²(t)

y = 53^1/2sin(2t) hence y'= 103^1/2 cos(2t)

therefore dy/dx = 103^1/2 cos(2t) / 4sec²(t). Since P is on point with x=43^1/2 we can duduce that t=π/3 and substituting t in dy/dx we get -53^1/2/16