# Differentiating expressions with both Symbolic arrays and Symbolic variables
**URL:** https://discourse.julialang.org/t/differentiating-expressions-with-both-symbolic-arrays-and-symbolic-variables/134522
**Category:** General Usage
**Tags:** question
**Created:** [December 12, 2025, 6:52pm UTC](https://discourse.julialang.org/t/differentiating-expressions-with-both-symbolic-arrays-and-symbolic-variables/134522 "2025-12-12T18:52:51Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@chenwilliam77](https://discourse.julialang.org/u/chenwilliam77)
#### Post date: [December 12, 2025, 6:52pm UTC](https://discourse.julialang.org/t/differentiating-expressions-with-both-symbolic-arrays-and-symbolic-variables/134522/1 "2025-12-12T18:52:51Z")
Here’s a MWE of what I want to work but doesn’t.
```julia-auto
using Symbolics
K = 3
@variables M[1:K, 1:K]
x1 = Symbolics.variables(:x1, 1:K)
x2 = Symbolics.variables(:x2, 1:K)
result = vcat(M * x1, M * x2)
Jx1 = Symbolics.jacobian(result, x1)
```
My understanding of the error is that, because M is a Symbolic matrix while x1 and x2 are vectors of Symbolic variables, M_x1 and M_x2 have type `SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}`. I assume that Symbolics doesn’t know how to tell that the result is a vector, so when I call vcat on these two objects, it doesn’t work. Now, a simple solution for me is to simply differentiate each expression on their own, but it’d be nice if I didn’t have to do that. I couldn’t figure out if Symbolics.jl has this functionality or not already.
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [December 12, 2025, 9:18pm UTC](https://discourse.julialang.org/t/differentiating-expressions-with-both-symbolic-arrays-and-symbolic-variables/134522/2 "2025-12-12T21:18:06Z")
We don’t hae symbolic array calculus yet, so it’ll need to scalarize to differentiate.
---
### Author:  [@brianguenter](https://discourse.julialang.org/u/brianguenter)
#### Post date: [December 12, 2025, 11:17pm UTC](https://discourse.julialang.org/t/differentiating-expressions-with-both-symbolic-arrays-and-symbolic-variables/134522/3 "2025-12-12T23:17:13Z")
You can do it in [FastDifferentiation](https://github.com/brianguenter/FastDifferentiation.jl):
```julia
julia> M = make_variables(:M,3,3)
3×3 Matrix{FastDifferentiation.Node}:
M1_1 M1_2 M1_3
M2_1 M2_2 M2_3
M3_1 M3_2 M3_3
julia> x1 = make_variables(:x1,3)
3-element Vector{FastDifferentiation.Node}:
x11
x12
x13
julia> x2 = make_variables(:x2,3)
3-element Vector{FastDifferentiation.Node}:
x21
x22
x23
julia> result = vcat(M*x1,M*x2)
6-element Vector{FastDifferentiation.Node}:
(((M1_1 * x11) + (M1_2 * x12)) + (M1_3 * x13))
(((M2_1 * x11) + (M2_2 * x12)) + (M2_3 * x13))
(((M3_1 * x11) + (M3_2 * x12)) + (M3_3 * x13))
(((M1_1 * x21) + (M1_2 * x22)) + (M1_3 * x23))
(((M2_1 * x21) + (M2_2 * x22)) + (M2_3 * x23))
(((M3_1 * x21) + (M3_2 * x22)) + (M3_3 * x23))
julia> Jx1 = jacobian(result,x1)
6×3 Matrix{FastDifferentiation.Node}:
M1_1 M1_2 M1_3
M2_1 M2_2 M2_3
M3_1 M3_2 M3_3
0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
```