[itex]\mathcal{L}_M(g_{kn}) = -\frac{1}{4\mu{0}}g_{kj} g_{nl} F^{kn} F^{jl} \\(adsbygoogle = window.adsbygoogle || []).push({});

\frac{\partial{\mathcal{L}_M}}{\partial{g_{kn}}}=-\frac{1}{4\mu_0}F^{pq}F^{jl} \frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})=+\frac{1}{4\mu_0} F^{pq} F^{lj} 2 \delta^k_p \delta^n_j g_{ql}[/itex]

I need to know how [itex]\frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql}) =

2\delta^k_p \delta^n_j g_{ql}

[/itex]. Can you explain how the final result on the right side was obtained?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Partial derivative with respect to metric tensor

Loading...

Similar Threads for Partial derivative respect |
---|

I Example of use of the Lie Derivative in Relativity |

I Lie and Covariant derivatives |

I Riemann curvature tensor derivation |

A Commutator of covariant derivative and D/ds on vector fields |

I Interesting Derivation of Maxwell's Equations |

**Physics Forums | Science Articles, Homework Help, Discussion**