diff --git a/exprtk.hpp b/exprtk.hpp
index 4ed4859..0517a91 100644
--- a/exprtk.hpp
+++ b/exprtk.hpp
@@ -32108,7 +32108,7 @@ namespace exprtk
    }
 
    template <typename T>
-   inline T third_derivative(expression<T>& e,
+   inline T third_derivative(const expression<T>& e,
                              T& x,
                              const T& h = T(0.0001))
    {
@@ -32127,7 +32127,7 @@ namespace exprtk
    }
 
    template <typename T>
-   inline T derivative(expression<T>& e,
+   inline T derivative(const expression<T>& e,
                        const std::string& variable_name,
                        const T& h = T(0.00000001))
    {
@@ -32154,7 +32154,7 @@ namespace exprtk
    }
 
    template <typename T>
-   inline T second_derivative(expression<T>& e,
+   inline T second_derivative(const expression<T>& e,
                               const std::string& variable_name,
                               const T& h = T(0.00001))
    {
@@ -32181,7 +32181,7 @@ namespace exprtk
    }
 
    template <typename T>
-   inline T third_derivative(expression<T>& e,
+   inline T third_derivative(const expression<T>& e,
                              const std::string& variable_name,
                              const T& h = T(0.0001))
    {