diff --git a/src/tracker/array.jl b/src/tracker/array.jl
index eb5d03c7..2b62883b 100644
--- a/src/tracker/array.jl
+++ b/src/tracker/array.jl
@@ -139,6 +139,13 @@ Base.sum(f::Union{Function,Type},xs::TrackedArray) = sum(f.(xs))
 
 back(::typeof(sum), Δ, xs::TrackedArray, dim...) = back(xs, similar(xs.data) .= Δ)
 
+Base.prod(xs::TrackedArray, dim) = track(prod, xs, dim)
+Base.prod(xs::TrackedArray) = track(prod, xs)
+Base.prod(f::Union{Function, Type}, xs::TrackedArray) = prod(f.(xs))
+
+back(::typeof(prod), Δ, xs::TrackedArray, dim...) = back(xs, similar(xs.data) .= (prod(xs.data, dim) ./ xs.data) .* Δ)
+back(::typeof(prod), Δ, xs::TrackedArray) = back(xs, similar(xs.data) .= (prod(xs.data) ./ xs.data) .* Δ)
+
 Base.maximum(xs::TrackedArray, args...) = maximum(xs.data, args...)
 Base.findfirst(xs::TrackedArray, args...) = findfirst(xs.data, args...)