# Unable To Partially Differentiate A Magnetic Field Equation Due To A Steady Current

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.

Your derivative is wrong, the result should be just $r^2/(r^2+x^2)^{3/2}$. –  enzotib Aug 23 '12 at 9:32