# Doubt on Cauchy Stress tensor: a partial derivative of metric tensor?

In the reference $$[1]$$ the author presented a definition of Stress tensor:

$$\sigma = 2 \rho \frac{\partial e}{\partial g} \tag{1}$$

In a local chart we have:

$$\sigma_{ab} = 2 \rho \frac{\partial e}{\partial g_{ab}} \tag{2}$$

So, $$\rho$$ is the mass density, $$e$$ the energy density and $$g$$ the metric tensor.

My question is: what suppose to mean the "metric derivative" $$\partial/ \partial g$$?

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$$[1]$$ MARSDEN.J, HUGHES.T.J.R; Mathematical Foundations of Elasticity. page 165. Thm 4.13.

• Do you understand the equation (2) and just the notation in equation (1) confuses you? Or both equations confuse you? – RenatoRenatoRenato Jan 19 at 14:55
• @RenatoRenatoRenato in fact I do not understand the derivative $\partial/ \partial g_{ab}$. Could be something in the context of tensor densities and derivative of metric determinant? – M.N.Raia Jan 19 at 14:58