I believe a source to source differentiator could deal with all these (where well defined of course), e.g.:

https://github.com/FluxML/Zygote.jl

    julia> fs = Dict("sin" => sin, "cos" => cos, "tan" => tan);
    
    julia> gradient(x -> fs[readline()](x), 1)
    sin
    0.5403023058681398