diff --git a/src/rule_definition_tools.jl b/src/rule_definition_tools.jl
index 911a32ddd..8d77955d1 100644
--- a/src/rule_definition_tools.jl
+++ b/src/rule_definition_tools.jl
@@ -158,6 +158,7 @@ end
 
 Compute the derivative of scalar function `f` at primal input point `xs...`,
 given that it had primal output `Ω`.
+
 Return a tuple of tuples with the partial derivatives of `f` with respect to the `xs...`.
 The derivative of the `i`-th component of `f` with respect to the `j`-th input can be
 accessed as `Df[i][j]`, where `Df = derivatives_given_output(Ω, f, xs...)`.
@@ -173,16 +174,43 @@ accessed as `Df[i][j]`, where `Df = derivatives_given_output(Ω, f, xs...)`.
 """
 function derivatives_given_output end
 
+"""
+    derivatives_given_output(f, xs...)
+
+Compute the derivative of scalar function `f` at primal input point `xs...`,
+when this is possible *without* knowing primal output `Ω`.
+
+!!! warning "Experimental"
+"""
+function derivatives_given_input end
+
 function scalar_derivative_expr(__source__, f, setup_stmts, inputs, partials)
-    return @strip_linenos quote
-        function ChainRulesCore.derivatives_given_output($(esc(:Ω)), ::Core.Typeof($f), $(inputs...))
+    given_output =  @strip_linenos quote
+        @inline function ChainRulesCore.derivatives_given_output($(esc(:Ω)), ::Core.Typeof($f), $(inputs...))
             $(__source__)
             $(setup_stmts...)
             return $(Expr(:tuple, partials...))
         end
     end
+    given_input = @strip_linenos quote
+        @inline function ChainRulesCore.derivatives_given_input(::Core.Typeof($f), $(inputs...))
+            $(__source__)
+            $(setup_stmts...)
+            return $(Expr(:tuple, partials...))
+        end
+    end
+    return if _free_of_omega([inputs, partials])
+        :($given_output; $given_input)
+    else
+        given_output
+    end
 end
 
+_free_of_omega(v::Union{Vector,Tuple}) = all(_free_of_omega, v)
+_free_of_omega(ex::Expr) = _free_of_omega(ex.args)
+_free_of_omega(s::Symbol) = s != :Ω
+_free_of_omega(other) = true # (@show other typeof(other); true)
+
 function scalar_frule_expr(__source__, f, call, setup_stmts, inputs, partials)
     n_outputs = length(partials)
     n_inputs = length(inputs)