diff --git a/src/lib.rs b/src/lib.rs
index 9bb0cef..69a5e55 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -179,7 +179,7 @@ pub fn lambert_w_m1(z: f64) -> Option<f64> {
 ///
 /// Uses the version of the Lambert W function with 50 bits of accuracy during the evaluation.
 ///
-/// # Example
+/// # Examples
 ///
 /// ```
 /// # use approx::assert_abs_diff_eq;
@@ -191,6 +191,12 @@ pub fn lambert_w_m1(z: f64) -> Option<f64> {
 ///
 /// assert_abs_diff_eq!(dw, 0.5 / (1.5 * x));
 /// ```
+/// Arguments smaller than -1/e (≈ -0.36787944117144233) result in `None`:
+/// ```
+/// # use approx::assert_abs_diff_eq;
+/// # use lambert_w::d_lambert_w_0;
+/// assert_eq!(d_lambert_w_0(-1.0), None);
+/// ```
 pub fn d_lambert_w_0(z: f64) -> Option<f64> {
     lambert_w_0(z).map(|w| {
         if z.abs() <= 0.1 {
@@ -218,6 +224,12 @@ pub fn d_lambert_w_0(z: f64) -> Option<f64> {
 ///
 /// assert_abs_diff_eq!(dw, 0.5 / (1.5 * x), epsilon = 1e-7);
 /// ```
+/// Arguments smaller than -1/e (≈ -0.36787944117144233) result in `None`:
+/// ```
+/// # use approx::assert_abs_diff_eq;
+/// # use lambert_w::sp_d_lambert_w_0;
+/// assert_eq!(sp_d_lambert_w_0(-1.0), None);
+/// ```
 pub fn sp_d_lambert_w_0(z: f64) -> Option<f64> {
     sp_lambert_w_0(z).map(|w| {
         if z.abs() <= 0.1 {