diff --git a/src/structural_transformation/pantelides.jl b/src/structural_transformation/pantelides.jl
index b6877d65f8..585c4a29d1 100644
--- a/src/structural_transformation/pantelides.jl
+++ b/src/structural_transformation/pantelides.jl
@@ -54,6 +54,7 @@ function pantelides_reassemble(state::TearingState, var_eq_matching)
             D(eq.lhs)
         end
         rhs = ModelingToolkit.expand_derivatives(D(eq.rhs))
+        rhs = fast_substitute(rhs, state.param_derivative_map)
         substitution_dict = Dict(x.lhs => x.rhs
         for x in out_eqs if x !== nothing && x.lhs isa Symbolic)
         sub_rhs = substitute(rhs, substitution_dict)
diff --git a/src/structural_transformation/symbolics_tearing.jl b/src/structural_transformation/symbolics_tearing.jl
index 552c6d13c3..548c7da519 100644
--- a/src/structural_transformation/symbolics_tearing.jl
+++ b/src/structural_transformation/symbolics_tearing.jl
@@ -65,7 +65,23 @@ function eq_derivative!(ts::TearingState{ODESystem}, ieq::Int; kwargs...)
 
     sys = ts.sys
     eq = equations(ts)[ieq]
-    eq = 0 ~ Symbolics.derivative(eq.rhs - eq.lhs, get_iv(sys); throw_no_derivative = true)
+    eq = 0 ~ fast_substitute(
+        ModelingToolkit.derivative(
+            eq.rhs - eq.lhs, get_iv(sys); throw_no_derivative = true), ts.param_derivative_map)
+
+    vs = ModelingToolkit.vars(eq.rhs)
+    for v in vs
+        # parameters with unknown derivatives have a value of `nothing` in the map,
+        # so use `missing` as the default.
+        get(ts.param_derivative_map, v, missing) === nothing || continue
+        _original_eq = equations(ts)[ieq]
+        error("""
+        Encountered derivative of discrete variable `$(only(arguments(v)))` when \
+        differentiating equation `$(_original_eq)`. This may indicate a model error or a \
+        missing equation of the form `$v ~ ...` that defines this derivative.
+        """)
+    end
+
     push!(equations(ts), eq)
     # Analyze the new equation and update the graph/solvable_graph
     # First, copy the previous incidence and add the derivative terms.
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index 73cdaba255..5927d3ebad 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -207,6 +207,7 @@ mutable struct TearingState{T <: AbstractSystem} <: AbstractTearingState{T}
     fullvars::Vector
     structure::SystemStructure
     extra_eqs::Vector
+    param_derivative_map::Dict{BasicSymbolic, Any}
 end
 
 TransformationState(sys::AbstractSystem) = TearingState(sys)
@@ -253,6 +254,12 @@ function Base.push!(ev::EquationsView, eq)
     push!(ev.ts.extra_eqs, eq)
 end
 
+function is_time_dependent_parameter(p, iv)
+    return iv !== nothing && isparameter(p) && iscall(p) &&
+           (operation(p) === getindex && is_time_dependent_parameter(arguments(p)[1], iv) ||
+            (args = arguments(p); length(args)) == 1 && isequal(only(args), iv))
+end
+
 function TearingState(sys; quick_cancel = false, check = true)
     sys = flatten(sys)
     ivs = independent_variables(sys)
@@ -264,6 +271,7 @@ function TearingState(sys; quick_cancel = false, check = true)
     var2idx = Dict{Any, Int}()
     symbolic_incidence = []
     fullvars = []
+    param_derivative_map = Dict{BasicSymbolic, Any}()
     var_counter = Ref(0)
     var_types = VariableType[]
     addvar! = let fullvars = fullvars, var_counter = var_counter, var_types = var_types
@@ -276,11 +284,23 @@ function TearingState(sys; quick_cancel = false, check = true)
 
     vars = OrderedSet()
     varsvec = []
+    eqs_to_retain = trues(length(eqs))
     for (i, eq′) in enumerate(eqs)
         if eq′.lhs isa Connection
             check ? error("$(nameof(sys)) has unexpanded `connect` statements") :
             return nothing
         end
+        if iscall(eq′.lhs) && (op = operation(eq′.lhs)) isa Differential &&
+           isequal(op.x, iv) && is_time_dependent_parameter(only(arguments(eq′.lhs)), iv)
+            # parameter derivatives are opted out by specifying `D(p) ~ missing`, but
+            # we want to store `nothing` in the map because that means `fast_substitute`
+            # will ignore the rule. We will this identify the presence of `eq′.lhs` in
+            # the differentiated expression and error.
+            param_derivative_map[eq′.lhs] = coalesce(eq′.rhs, nothing)
+            eqs_to_retain[i] = false
+            # change the equation if the RHS is `missing` so the rest of this loop works
+            eq′ = eq′.lhs ~ coalesce(eq′.rhs, 0.0)
+        end
         if _iszero(eq′.lhs)
             rhs = quick_cancel ? quick_cancel_expr(eq′.rhs) : eq′.rhs
             eq = eq′
@@ -295,6 +315,12 @@ function TearingState(sys; quick_cancel = false, check = true)
             any(isequal(_var), ivs) && continue
             if isparameter(_var) ||
                (iscall(_var) && isparameter(operation(_var)) || isconstant(_var))
+                if is_time_dependent_parameter(_var, iv) &&
+                   !haskey(param_derivative_map, Differential(iv)(_var))
+                    # Parameter derivatives default to zero - they stay constant
+                    # between callbacks
+                    param_derivative_map[Differential(iv)(_var)] = 0.0
+                end
                 continue
             end
             v = scalarize(v)
@@ -351,6 +377,9 @@ function TearingState(sys; quick_cancel = false, check = true)
             eqs[i] = eqs[i].lhs ~ rhs
         end
     end
+    eqs = eqs[eqs_to_retain]
+    neqs = length(eqs)
+    symbolic_incidence = symbolic_incidence[eqs_to_retain]
 
     ### Handle discrete variables
     lowest_shift = Dict()
@@ -438,7 +467,7 @@ function TearingState(sys; quick_cancel = false, check = true)
     ts = TearingState(sys, fullvars,
         SystemStructure(complete(var_to_diff), complete(eq_to_diff),
             complete(graph), nothing, var_types, sys isa AbstractDiscreteSystem),
-        Any[])
+        Any[], param_derivative_map)
     if sys isa DiscreteSystem
         ts = shift_discrete_system(ts)
     end
diff --git a/test/state_selection.jl b/test/state_selection.jl
index b8404d1f26..a8d3e57773 100644
--- a/test/state_selection.jl
+++ b/test/state_selection.jl
@@ -2,7 +2,7 @@ using ModelingToolkit, OrdinaryDiffEq, Test
 using ModelingToolkit: t_nounits as t, D_nounits as D
 
 sts = @variables x1(t) x2(t) x3(t) x4(t)
-params = @parameters u1(t) u2(t) u3(t) u4(t)
+params = @parameters u1 u2 u3 u4
 eqs = [x1 + x2 + u1 ~ 0
        x1 + x2 + x3 + u2 ~ 0
        x1 + D(x3) + x4 + u3 ~ 0
diff --git a/test/structural_transformation/utils.jl b/test/structural_transformation/utils.jl
index 8894f0bbc9..6c5a564e9f 100644
--- a/test/structural_transformation/utils.jl
+++ b/test/structural_transformation/utils.jl
@@ -5,6 +5,7 @@ using SparseArrays
 using UnPack
 using ModelingToolkit: t_nounits as t, D_nounits as D, default_toterm
 using Symbolics: unwrap
+using DataInterpolations
 const ST = StructuralTransformations
 
 # Define some variables
@@ -282,3 +283,111 @@ end
         @test length(mapping) == 3
     end
 end
+
+@testset "Issue#3480: Derivatives of time-dependent parameters" begin
+    @component function FilteredInput(; name, x0 = 0, T = 0.1)
+        params = @parameters begin
+            k(t) = x0
+            T = T
+        end
+        vars = @variables begin
+            x(t) = k
+            dx(t) = 0
+            ddx(t)
+        end
+        systems = []
+        eqs = [D(x) ~ dx
+               D(dx) ~ ddx
+               dx ~ (k - x) / T]
+        return ODESystem(eqs, t, vars, params; systems, name)
+    end
+
+    @component function FilteredInputExplicit(; name, x0 = 0, T = 0.1)
+        params = @parameters begin
+            k(t)[1:1] = [x0]
+            T = T
+        end
+        vars = @variables begin
+            x(t) = k
+            dx(t) = 0
+            ddx(t)
+        end
+        systems = []
+        eqs = [D(x) ~ dx
+               D(dx) ~ ddx
+               D(k[1]) ~ 1.0
+               dx ~ (k[1] - x) / T]
+        return ODESystem(eqs, t, vars, params; systems, name)
+    end
+
+    @component function FilteredInputErr(; name, x0 = 0, T = 0.1)
+        params = @parameters begin
+            k(t) = x0
+            T = T
+        end
+        vars = @variables begin
+            x(t) = k
+            dx(t) = 0
+            ddx(t)
+        end
+        systems = []
+        eqs = [D(x) ~ dx
+               D(dx) ~ ddx
+               dx ~ (k - x) / T
+               D(k) ~ missing]
+        return ODESystem(eqs, t, vars, params; systems, name)
+    end
+
+    @named sys = FilteredInputErr()
+    @test_throws ["derivative of discrete variable", "k(t)"] structural_simplify(sys)
+
+    @mtkbuild sys = FilteredInput()
+    vs = Set()
+    for eq in equations(sys)
+        ModelingToolkit.vars!(vs, eq)
+    end
+    for eq in observed(sys)
+        ModelingToolkit.vars!(vs, eq)
+    end
+
+    @test !(D(sys.k) in vs)
+
+    @mtkbuild sys = FilteredInputExplicit()
+    obsfn1 = ModelingToolkit.build_explicit_observed_function(sys, sys.ddx)
+    obsfn2 = ModelingToolkit.build_explicit_observed_function(sys, sys.dx)
+    u = [1.0]
+    p = MTKParameters(sys, [sys.k => [2.0], sys.T => 3.0])
+    @test obsfn1(u, p, 0.0) ≈ (1 - obsfn2(u, p, 0.0)) / 3.0
+
+    @testset "Called parameter still has derivative" begin
+        @component function FilteredInput2(; name, x0 = 0, T = 0.1)
+            ts = collect(0.0:0.1:10.0)
+            spline = LinearInterpolation(ts .^ 2, ts)
+            params = @parameters begin
+                (k::LinearInterpolation)(..) = spline
+                T = T
+            end
+            vars = @variables begin
+                x(t) = k(t)
+                dx(t) = 0
+                ddx(t)
+            end
+            systems = []
+            eqs = [D(x) ~ dx
+                   D(dx) ~ ddx
+                   dx ~ (k(t) - x) / T]
+            return ODESystem(eqs, t, vars, params; systems, name)
+        end
+
+        @mtkbuild sys = FilteredInput2()
+        vs = Set()
+        for eq in equations(sys)
+            ModelingToolkit.vars!(vs, eq)
+        end
+        for eq in observed(sys)
+            ModelingToolkit.vars!(vs, eq)
+        end
+
+        @test D(sys.k(t)) in vs
+    end
+end