1. The problem statement, all variables and given/known data Hello, I am supposed to show that the quantity TR=JTF-t satisfies TR=∂W/∂F for some scalar function W(X, F, θ) in my continuum mechanics homework. The task is to identify this scalar function W(X, F, θ). 2. Relevant equations This is part b) of a question. In part a), we get the following results which may or may not be relevant to the solution of the problem: Constitutive equations are: T=T(F,θ) η=η(F,θ) A=A(F,θ) q=q(F,θ,gradθ) where η = -∂A/∂θ TF-T = ρ*∂A/∂F 3. The attempt at a solution By substitution of the results in 2., I got TR=JTF-t =J*ρ*∂A/∂F =ρR(X)*∂A(F,θ)/∂F(X) Is it as easy as saying that W(X, F, θ) = ρR(X)*A(F,θ) ? That's the solution I got but it seems too easy/I'm unsure... :D I would greatly appreciate any advice. Thank you so so much!!!