differentiation of Strain energy Function

Dear,
I am having problem to find "Cauchy stress(σ) " and " Spatial elastic Tensor (c)" from the "strain energy function (ψ)" using 2nd Piola Kirchhoff stress ( S) of transversely isotropic hyper-elastic material. as per the Mechanics the 

how this differentiation is done? if you have any literature for this then it is requested to provide the same.

my equation for strain energy function is

Regards

Abhishek Kumar
Asso. Prof.
MED
FET, MRIU