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symbolic differentiation to find analytical expressions that are time-consuming to calculate manually?

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Given a function of two variables
f(x,y) =
I want to find the analytial expression of the determinant of the Hessian of f. are real numbers that I can not specify further, and are scalar functions that I also can not specify further because they depend on n.
If I compute, for instance, the partial derivatives on a paper, I would write
It is quite time-consuming and messy to do similar calculations manually on a paper.
I know that symbolic differentiation can be used in a context like
syms x
f = x^2
diff(f,x) =
but can it also be applied to expressions that are not completely defined like in my context?
SA-W on 6 Jun 2023
But the E_i are not convex. In 1d, the N_i resemble hat-functions which are not convex.
So I think I have to incorporate "convexity" via the E_i.

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