If `y = x `log ` |x + sqrt(1 + x ^(2)) |- sqrt(1 + x ^(2)) ` then ` (dy )/(dx )=`

If y = log ((sqrt(1 + x^(2)) + x)/(sqrt(1 + x^(2)) -x)) " then " (dy)/(dx) = ?

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

If y = log (x + sqrt(x^(2)+1) then dy/dx =

If y= log (x + sqrt(x^(2) + a^(2))) then (dy)/(dx) = ………

If y = log (x + sqrt(x^(2) + a^(2))) " then " (dy)/(dx) = ?

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

If y = (x sin^(-1) x)/(sqrt(1 - x^2)) + "log" sqrt(1 - x^2) , prove that (dy)/(dx) = (sin^(-1)x)/((1 - x^2)^(3//2))

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

If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2) , show that (1 - x^2) (dy)/(dx) + xy + 1 = 0