diff --git a/src/polynomials/standard-basis/immutable-polynomial.jl b/src/polynomials/standard-basis/immutable-polynomial.jl
index aeadfbaf..a1749e23 100644
--- a/src/polynomials/standard-basis/immutable-polynomial.jl
+++ b/src/polynomials/standard-basis/immutable-polynomial.jl
@@ -142,8 +142,11 @@ end
 
 # special cases are much more performant
 derivative(p::ImmutableDensePolynomial{B,T,X,0}) where {B<:StandardBasis,T,X} = p
+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)