higher-order derivatives

[ohno]

Are there any functions or issues related to higher derivatives?

I extended derivative() to support higher derivatives in preparation for the implementation of Taylor series (#59). I replaced

Symbolics.jl/src/diff.jl

Lines 420 to 426 in c0966fb

	function derivative(O, v; simplify=false)
	if O isa AbstractArray
	Num[Num(expand_derivatives(Differential(v)(value(o)), simplify)) for o in O]
	else
	Num(expand_derivatives(Differential(v)(value(O)), simplify))
	end
	end

with

function derivative(O, v; simplify=false, n=1)
    D = n==0 ? v->v : Differential(v)^n
    if O isa AbstractArray
        Num[Num(expand_derivatives(D(Symbolics.value(o)), simplify)) for o in O]
    else
        Num(expand_derivatives(D(Symbolics.value(O)), simplify))
    end
end

to support $n$ th-order derivatives. For example, first-order derivatives are following.

julia> derivative([sin(x), cos(x)], x)
2-element Vector{Num}:
  cos(x)
 -sin(x)

Also, second-order derivatives are following.

julia> derivative([sin(x), cos(x)], x, n=2)
2-element Vector{Num}:
 -sin(x)
 -cos(x)

If you like this I will send a pull request.