diff --git a/Project.toml b/Project.toml
index cd2612f3c..4df6346eb 100644
--- a/Project.toml
+++ b/Project.toml
@@ -68,7 +68,8 @@ Distributions = "0.25"
 DocStringExtensions = "0.9"
 DomainSets = "0.6, 0.7"
 DynamicPolynomials = "0.5, 0.6"
-ForwardDiff = "0.10.36"
+FiniteDiff = "2"
+ForwardDiff = "0.10.36, 1"
 Groebner = "0.8.2, 0.9"
 LaTeXStrings = "1.3"
 LambertW = "1.0.0"
@@ -100,6 +101,7 @@ julia = "1.10"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
 DynamicQuantities = "06fc5a27-2a28-4c7c-a15d-362465fb6821"
+FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
 LambertW = "984bce1d-4616-540c-a9ee-88d1112d94c9"
@@ -113,4 +115,4 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "SafeTestsets", "Pkg", "PkgBenchmark", "PreallocationTools", "ForwardDiff", "Groebner", "BenchmarkTools", "ReferenceTests", "Random", "LambertW", "Lux", "ComponentArrays", "Nemo", "DynamicQuantities"]
+test = ["Test", "SafeTestsets", "Pkg", "PkgBenchmark", "PreallocationTools", "ForwardDiff", "Groebner", "BenchmarkTools", "ReferenceTests", "Random", "LambertW", "Lux", "ComponentArrays", "Nemo", "DynamicQuantities","FiniteDiff"]
diff --git a/src/diff.jl b/src/diff.jl
index e72465c63..68cf26ca9 100644
--- a/src/diff.jl
+++ b/src/diff.jl
@@ -480,6 +480,9 @@ for (modu, fun, arity) ∈ DiffRules.diffrules(; filter_modules=(:Base, :Special
     end
 end
 
+derivative(::typeof(mod), args::NTuple{2, Any}, ::Val{1}) = ifelse(mod(args...) == 0, NaN, 1)
+derivative(::typeof(mod), args::NTuple{2, Any}, ::Val{2}) = ifelse(mod(args...) == 0, NaN, -floor(args[1] / args[2]))
+
 derivative(::typeof(+), args::NTuple{N,Any}, ::Val) where {N} = 1
 derivative(::typeof(*), args::NTuple{N,Any}, ::Val{i}) where {N,i} = *(deleteat!(collect(args), i)...)
 derivative(::typeof(one), args::Tuple{<:Any}, ::Val) = 0
diff --git a/test/diff.jl b/test/diff.jl
index fb75e648d..1288d106f 100644
--- a/test/diff.jl
+++ b/test/diff.jl
@@ -1,6 +1,7 @@
 using Symbolics
 using Test
 using Symbolics: value
+using FiniteDiff
 
 # Derivatives
 @variables t σ ρ β
@@ -604,3 +605,13 @@ let
     @test isequal(expand_derivatives(Dt(y[1])), Dt(x) * Dx(y[1])) # same for vector var
     @test isequal(expand_derivatives(Dt(Y[1,1])), Dt(x) * Dx(Y[1,1])) # same for matrix arr
 end
+
+@testset "Derivative of mod function" begin
+    f(x, y) = mod(x, y)
+
+   @test isnan(Symbolics.derivative(mod, (4, 2), Val(1)))  
+   @test Symbolics.derivative(mod, (5.0, 2.0), Val(1)) == FiniteDiff.finite_difference_derivative(x -> f(x, 2.0), 5.0)
+
+   @test isnan(Symbolics.derivative(mod, (4, 2), Val(2)))  
+   @test Symbolics.derivative(mod, (5.0, 2.0), Val(2)) == FiniteDiff.finite_difference_derivative(y -> f(5.0, y), 2.0)
+end