If `x=sin^(-1)((t)/(sqrt(1+t^(2)))),y=cos^(-1)((1)/(sqrt(1+t^(2)))),"show that "(dy)/(dx)=1`

If x=sin^(-1)((2t)/(1+t^(2)))andy=tan^(-1)((2t)/(1-t^(2))), then prove that (dy)/(dx)=1 .

If x=sin^(-1)((2t)/(1+t^(2))) and y=tan^(-1)((2t)/(1-t^(2))),t>1. Prove that (dy)/(dx)=-1

If x=sin^(-1)(3t-4t^(3)) and y=cos^(-1)sqrt(1-t^(2)) then (dy)/(dx)=

Derivative of sin^(-1)((t)/(sqrt(1+t^(2)))) with respect to cos^(-1)((1)/(sqrt(1+t^(2))) is

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

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

If x= sin^(-1)(3t-4t^(3)) and y=cos^(-1)(sqrt(1-t^(2))) , then (dy)/(dx) is equal to

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

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