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independent variable derivative in piece-wise function

Good day all,

Lets say I am solving a general form PDE for a variable 'u' and I define some piece-wise function in terms of 'u' (i.e. pw1(u)).

My question is, it is possible to evaluate the spatial derivative of 'u' within the definition of this piece-wise function? i.e.

pw1(u) = F(ux,uy) where 'F' is some expression in the piece-wise function definition that is a function of grad(u)

Is there a clever or optimized way of implementing this?

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