If `x=cost andy=sint`, then prove that `(dy)/(dx)=(1)/(sqrt3),` at `t=(2pi)/(3)`.

If x=a(t+1/t) and y=a(t-1/t) , prove that (dy)/(dx)=x/y

If y=(tanx)^((tanx)^((tanx)^...oo)), then prove that (dy)/(dx)=2 at x=(pi)/(4).

If y=|cosx|+|sinx| , then (dy)/(dx)" at "x=(2pi)/(3) is

If y= {x + sqrt(x^(2) + a^(2))}^(n) prove that (dy)/(dx)= (ny)/(sqrt(x^(2) + a^(2))). n gt 1 ne N

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

If y= sin^(-1)x then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x (dy)/(dx)=0

If y=xlog(x/(a+bx)) , then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If x=e^(-t^(2)), y=tan^(-1)(2t+1) , then (dy)/(dx)=