[log(x+sqrt(1+x^(2)))],[" exprement wier negrect to "x]

log (x+sqrt(x^2-1))

(log(x+sqrt(x^(2)+1)))/(x) is

log(sqrt(x)+1/sqrt(x))

f(x)=2x-tan^(-1)x-log(x+sqrt(1+x^(2)))(x>0) is increasing in

If y=log[x+sqrt((1+x^(2)))], prove that sqrt((1+x^(2)))(dy)/(dx)=1

If y=sqrt(log x+sqrt(log x +sqrt(log x+....oo))) " then prove that " dy/dx = 1/(x(2y-1)).

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