I have to find the derivative of $\displaystyle x(x^2+1)$^(1/2)

The problem is, I thought the chain rule was deriv. of outside (leave inside alone) multiplied by the deriv. of the inside.

So, I had

1/2$\displaystyle x(x^2+1)$^(-1/2) $\displaystyle * (2x)$

yet when I test it in my calculator, it is wrong, what am I missing?