" (a) "quad y=tan^(-1)(sqrt(1+t^(2))+sqrt(1-t^(2)))/(sqrt(1+t^(2))-sqrt(1-t^(2)))quad 2tan(dy)/(dt)quad A sqrt(24)quad 26}

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) .

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

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

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

int_(0)^(1)t^(5)*sqrt(1-t^(2))*dt

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

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