diff --git a/DifferentiationInterface/src/second_order/hessian.jl b/DifferentiationInterface/src/second_order/hessian.jl
index 5067f78c2..84bbcad20 100644
--- a/DifferentiationInterface/src/second_order/hessian.jl
+++ b/DifferentiationInterface/src/second_order/hessian.jl
@@ -12,7 +12,7 @@ function prepare_hessian(
 end
 
 """
-    prepare!_hessian(f, backend, x, [contexts...]) -> new_prep
+    prepare!_hessian(f, prep, backend, x, [contexts...]) -> new_prep
 
 $(docstring_prepare!("hessian"))
 """
diff --git a/DifferentiationInterface/src/second_order/hvp.jl b/DifferentiationInterface/src/second_order/hvp.jl
index 58afeadbf..068781727 100644
--- a/DifferentiationInterface/src/second_order/hvp.jl
+++ b/DifferentiationInterface/src/second_order/hvp.jl
@@ -17,9 +17,9 @@ function prepare_hvp(
 end
 
 """
-    prepare!_hvp(f, backend, x, tx, [contexts...]) -> new_prep
+    prepare!_hvp(f, prep, backend, x, tx, [contexts...]) -> new_prep
 
-$(docstring_prepare("hvp"))
+$(docstring_prepare!("hvp"))
 """
 function prepare!_hvp(
         f::F,