Given that $H = \pm \frac{I}{2}\frac{\partial}{\partial x}(\frac{x}{\sqrt{r^2+x^2}})$
I need to prove that $H = \pm \frac{r^2I}{2\sqrt{(r^2+x^2)^3}}$ where $H$ is the magnetic field vector due to a steady current $I$ flowing around a circular wire of radius $r$ and at a distance $x$ from its centre.
I could manage to partially differentiate $\frac{\partial}{\partial x}(\frac{x}{\sqrt{r^2+x^2}}) = \sqrt{r^2+x^2}-x^2$ after using the quotient rule and a little bit of simplification.
Please help as I am unable to prove the above expression.
Thank You.