I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ?

$$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} \left(2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}-2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\lambda}}{\partial x_{\sigma}}\right)$$

The answer is

$$4\dfrac{\partial A_{\mu}}{\partial x_{\nu}}-4\dfrac{\partial A_{\nu}}{\partial x_{\mu}}$$

where $A$ is vector potential and $x$ is four-vector.

  • $\begingroup$ What have you tried, why doesn't it work, and what concept are you having trouble with when you try to understand why it doesn't work? $\endgroup$ – David Z Mar 13 '14 at 18:15
  • 1
    $\begingroup$ Hint: try writing $\frac{\partial A_\mu}{\partial x_\lambda}=T_\mu^\lambda$ and similarly for different indices. $\endgroup$ – Danu Mar 13 '14 at 18:22

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