Find the derivative of square root (x) ln x

I use the product rule and get: sqr root(x) * 1/x + 1/2x^(-1/2) ln x
then how do you simplify this?
my friend is getting x^(-1/2) + 1/(2sqroot (x)) ln x.... but isn't that missing the (1/x)
help please i'm majorly confused!

It isn't missing.
sqrt(x) = x^(1/2)

So sqrt(x)/x = x^(1/2) / x = x^(1/2 - 1) = x^(-1/2).