diff --git a/src/polynomials/standard-basis/immutable-polynomial.jl b/src/polynomials/standard-basis/immutable-polynomial.jl
index a1749e23..01e5a003 100644
--- a/src/polynomials/standard-basis/immutable-polynomial.jl
+++ b/src/polynomials/standard-basis/immutable-polynomial.jl
@@ -145,8 +145,6 @@ derivative(p::ImmutableDensePolynomial{B,T,X,0}) where {B<:StandardBasis,T,X} =
 derivative(p::ImmutableDensePolynomial{B,T,X,1}) where {B<:StandardBasis,T,X} = zero(p)
 
 function derivative(p::ImmutableDensePolynomial{B,T,X,N}) where {B<:StandardBasis,T,X,N}
-    N == 0 && return p
-    N == 1 && return zero(p)
     hasnan(p) && return ImmutableDensePolynomial{B,T,X,1}(zero(T)/zero(T)) # NaN{T}
     cs = ntuple(i -> i*p.coeffs[i+1], Val(N-1))
     R = eltype(cs)
diff --git a/test/StandardBasis.jl b/test/StandardBasis.jl
index f9ef0784..3f45e594 100644
--- a/test/StandardBasis.jl
+++ b/test/StandardBasis.jl
@@ -1094,6 +1094,15 @@ end
         @test_throws ArgumentError derivative(pR, -1)
         @test integrate(P([1,1,0,0]), 0, 2) == 4.0
 
+        p₀, p₁, p₂ = zero(P), one(P), variable(P)
+        @test derivative(p₂) == p₁
+        @test derivative(p₁) == p₀
+        @test integrate(p₀, 1) == p₁
+        @test integrate(p₁) == p₂
+        if P != Polynomials.MutableSparseVectorPolynomial{Polynomials.StandardBasis}
+            @test repr(derivative(p₁)) == string(P)*"(0.0)" # #615 display issue
+        end
+
         P <: FactoredPolynomial && continue
 
         @testset for i in 1:10