Find y prime for Function

Find y prime for given function.

y = (-sqrt{x^2+2})/(x) + ln(x + sqrt{x^2+2})

let be u(x) = √(x² + 2)
u' = x/√(x² + 2)
u' = x/u

rewrite function as
y = -u(1/x) + ln(x + u)

y' = -u'(1/x) - u(-1/x²) + (1 + u')/(x + u)

y' = -(x/u)(1/x) + u/x² + (1 +x/u)/(x + u)

y' = -1/u + u/x² + ((u + x)/u)/(x + u)

y' = -1/u + u/x² + 1/u

y' = u/x²

y' = (√(x² + 2))/x²