Defining a function using the output of another function

General Usage
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2

I’m not sure if I understood the problem correctly, but perhaps just pass the coefficients and offsets as parameters? Something like

function dy(y, δx, coeffs, offsets)
    N = length(y)
    dy = zeros(N)
    for j in eachindex(y)
        denom = 32*δx  # and something else near the edges?
        dy[j] = sum(y[j+i]*c for (i,c) in zip(offsets,coeffs) if j+i in eachindex(y)) / denom
    end
    dy
end

(I’m not sure what that denominator is for and where the numbers 32,8,2 come from).
You might want to take a look at ImageFiltering.jl, and specifically ImageFiltering.imfilter. It does exactly what it seems you are trying to do, except maybe near the edges (since I’m not sure what is going on near the edges in your code).