if `x=sqrt((1-t^2)/(1+t^2)) , y={sqrt(1+t^2)-sqrt(1-t^2)}/{sqrt(1+t^2)+sqrt(1-t^2)}` then `(dy)/(dx)`

If x=sqrt((1-t^(2))/(1+t^(2))) and y=(sqrt(1+t^(2))-sqrt(1-t^(2)))/(sqrt(1+t^(2))+sqrt(1-t^(2))) then (d^(2)y)/(dx^(2))=

If x = sqrt((1-t^(2))/(1+t^(2)) and y = (sqrt(1+t^(2))-sqrt(1-t^(2)))/(sqrt(1+t^(2)) + sqrt(1-t^(2))) then (d^(2)y)/(dx^(2)) =

If y=tan^(-1) [(sqrt(1+t^(2))+sqrt(1-t^(2)))/(sqrt(1+t^(2))-sqrt(1-t^(2)))] , find the value of (dy)/(dt) .

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a n dtany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) and tan (y/2)=sqrt((1-t)/(1+t)) then (dy)/dx at t=1/2 is

e^(x)=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) andtan (y)/(2)=sqrt((1-t)/(1+t)) then (dy)/(dx) at t=(1)/(2) is (a)-(1)/(2) (b) (1)/(2)(c)0(d) none of these

Find (dx)/(dt) when x = sin^-1(t.sqrt(1-t) +sqrt(t) sqrt(1-t^2)) .