Derivative of Riemann tensor respect to Riemann tensor

I know that, for example we have

$$frac{delta g^{jk}}{delta g^{lm}}=delta^{j}_{(l}delta^{k}_{m)}.$$
This topic was discussed previously e.g. on Physicsforums.com and on Phys.SE.

So I was wondering, how can I compute
$frac{delta R^{j}_{klm}}{delta R^{a}_{bcd}}$?

And in general, how can I compute this quantity for a tensor with some symmetries?