What is the Partial Derivative of Metric in Gravitational Action?

[krishna mohan]

Could someone tell me what would be the partial derivative...

$$\frac{ d g_{ab} }{ d g_{cd}}$$

??
Such expressions occur when one does variations of gravitational action...

Note: For some reason, the d needed for derivative is not appearing in the post...although it was visible in the preview...

 

[Bill_K]

Depends on exactly what you're doing, but if you're doing a variation in which all 10 components of g are independent, then your expression is equal to δ_ac δ_bd, or more precisely the symmetrized version of that,
(δ_ac δ_bd + δ_ad δ_bc)/2

 

[krishna mohan]

Okay...

But if a is not equal to b, then won't the symmetrised version have an unwanted factor of (1/2)?

i.e if a=c and b=d, one would like to have 1 as the answer...but the symmetrised version would give 1/2...