If x= a(cos t +t sin t) and y=a(sin t - t cos t), find `(d^2y)/(dx^2)`

If x = 2 cos t - cos 2 t and y =2 sin t - sin 2t, then (dy)/(dx) at t = (pi)/(2) is

Find dy/dx if x=a(t-sin t) , y=a(1-cost) .

If x = sin t and y = tan t , then (dy)/(dx) is equal to a) cos ^(2) t b) (1)/( cos ^(3) t ) c) (1)/( cos ^(2) t ) d) sin ^(2) t

Find dy/dx if x=a(cost+logtan(t//2)) and y=a sin t

If x = ( 3t)/( 1 + t ^(3)) and y = ( 3 t ^(2))/( 1 +t ^(3)), then (dy)/(dx) at t =1 equals

If x= A cos 4t + B sin 4t , then (d^(2)x)/(dt^(2))=

If x=sqrt(a^(sin^-1 t) , y=sqrt(a^(cos^-1 t) Show that dy/dx=(-y)/x