diff --git a/crates/bevy_math/src/common_traits.rs b/crates/bevy_math/src/common_traits.rs
index a9a8ef910a..4e127f4026 100644
--- a/crates/bevy_math/src/common_traits.rs
+++ b/crates/bevy_math/src/common_traits.rs
@@ -80,6 +80,8 @@ impl VectorSpace for f32 {
 ///
 /// [vector spaces]: VectorSpace
 #[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
+#[cfg_attr(feature = "bevy_reflect", derive(bevy_reflect::Reflect))]
 pub struct Sum<V, W>(pub V, pub W);
 
 impl<V, W> Mul<f32> for Sum<V, W>
@@ -424,6 +426,9 @@ pub trait HasTangent {
 }
 
 /// A value with its derivative.
+#[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
+#[cfg_attr(feature = "bevy_reflect", derive(bevy_reflect::Reflect))]
 pub struct WithDerivative<T>
 where
     T: HasTangent,
@@ -436,6 +441,9 @@ where
 }
 
 /// A value together with its first and second derivatives.
+#[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
+#[cfg_attr(feature = "bevy_reflect", derive(bevy_reflect::Reflect))]
 pub struct WithTwoDerivatives<T>
 where
     T: HasTangent,
diff --git a/crates/bevy_math/src/curve/derivatives/mod.rs b/crates/bevy_math/src/curve/derivatives/mod.rs
index d819443f0d..5949d356e2 100644
--- a/crates/bevy_math/src/curve/derivatives/mod.rs
+++ b/crates/bevy_math/src/curve/derivatives/mod.rs
@@ -37,24 +37,28 @@ use bevy_reflect::{FromReflect, Reflect};
 /// derivatives to be extracted along with values.
 ///
 /// This is implemented by implementing [`SampleDerivative`].
-pub trait CurveWithDerivative<T>: SampleDerivative<T>
+pub trait CurveWithDerivative<T>: SampleDerivative<T> + Sized
 where
     T: HasTangent,
 {
     /// This curve, but with its first derivative included in sampling.
-    fn with_derivative(self) -> impl Curve<WithDerivative<T>>;
+    ///
+    /// Notably, the output type is a `Curve<WithDerivative<T>>`.
+    fn with_derivative(self) -> SampleDerivativeWrapper<Self>;
 }
 
 /// Trait for curves that have a well-defined notion of second derivative,
 /// allowing for two derivatives to be extracted along with values.
 ///
 /// This is implemented by implementing [`SampleTwoDerivatives`].
-pub trait CurveWithTwoDerivatives<T>: SampleTwoDerivatives<T>
+pub trait CurveWithTwoDerivatives<T>: SampleTwoDerivatives<T> + Sized
 where
     T: HasTangent,
 {
     /// This curve, but with its first two derivatives included in sampling.
-    fn with_two_derivatives(self) -> impl Curve<WithTwoDerivatives<T>>;
+    ///
+    /// Notably, the output type is a `Curve<WithTwoDerivatives<T>>`.
+    fn with_two_derivatives(self) -> SampleTwoDerivativesWrapper<Self>;
 }
 
 /// A trait for curves that can sample derivatives in addition to values.
@@ -210,7 +214,7 @@ where
     T: HasTangent,
     C: SampleDerivative<T>,
 {
-    fn with_derivative(self) -> impl Curve<WithDerivative<T>> {
+    fn with_derivative(self) -> SampleDerivativeWrapper<Self> {
         SampleDerivativeWrapper(self)
     }
 }
@@ -220,7 +224,7 @@ where
     T: HasTangent,
     C: SampleTwoDerivatives<T> + CurveWithDerivative<T>,
 {
-    fn with_two_derivatives(self) -> impl Curve<WithTwoDerivatives<T>> {
+    fn with_two_derivatives(self) -> SampleTwoDerivativesWrapper<Self> {
         SampleTwoDerivativesWrapper(self)
     }
 }