Question 180822
g(x) = xln(x + sqrt(1 + x^2)) - sqrt(1 + x^2)


Let z=sqrt(1 + x^2) ----> z'=x/(sqrt(1+x^2))


g(x) = xln(x + z) - z



g'(x) = (x*z')/(x + z) - ln(x+z) - z'



g'(x) = (x*(x/(sqrt(1+x^2))))/(x + sqrt(1 + x^2)) - ln(x+sqrt(1+x^2)) - x/(sqrt(1+x^2))



g'(x) = ln(x+sqrt(1+x^2))