" 14.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 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)

intt^(2)sqrt(1-t)*dt

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)) =

intt^(2)sqrt(1-t)dt

I=int sqrt(1-t^(2))dt

(-1)/(2)int(dt)/(sqrt(1-t)sqrt(t))

Evaluate int(t^(2))/(sqrt(1-t^(2)))dt

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) =

" (a) "int(dt)/(sqrt(1-t^(2)))