diff --git a/src/main/java/org/apache/commons/math/analysis/function/Acos.java b/src/main/java/org/apache/commons/math/analysis/function/Acos.java
index bce111474..97f029036 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Acos.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Acos.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Acos implements UnivariateRealFunction {
+public class Acos implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.acos(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return -1 / FastMath.sqrt(1 - x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Acosh.java b/src/main/java/org/apache/commons/math/analysis/function/Acosh.java
index 352ee3460..c6d72089e 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Acosh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Acosh.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Acosh implements UnivariateRealFunction {
+public class Acosh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.acosh(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / FastMath.sqrt(x * x - 1);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Asin.java b/src/main/java/org/apache/commons/math/analysis/function/Asin.java
index 8ffe80c4b..c4edf7408 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Asin.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Asin.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Asin implements UnivariateRealFunction {
+public class Asin implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.asin(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / FastMath.sqrt(1 - x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Asinh.java b/src/main/java/org/apache/commons/math/analysis/function/Asinh.java
index 465d72ddc..40eae84f8 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Asinh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Asinh.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Asinh implements UnivariateRealFunction {
+public class Asinh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.asinh(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / FastMath.sqrt(1 + x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Atan.java b/src/main/java/org/apache/commons/math/analysis/function/Atan.java
index bd0379a26..7a2b702c8 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Atan.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Atan.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Atan implements UnivariateRealFunction {
+public class Atan implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.atan(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / (1 + x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Atanh.java b/src/main/java/org/apache/commons/math/analysis/function/Atanh.java
index 6ac3fb3ba..e851e1997 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Atanh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Atanh.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Atanh implements UnivariateRealFunction {
+public class Atanh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.atanh(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / (1 - x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Cbrt.java b/src/main/java/org/apache/commons/math/analysis/function/Cbrt.java
index f5b3c9bfe..c682b691c 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Cbrt.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Cbrt.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Cbrt implements UnivariateRealFunction {
+public class Cbrt implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.cbrt(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / (3 * FastMath.cbrt(x * x));
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Constant.java b/src/main/java/org/apache/commons/math/analysis/function/Constant.java
index 563197cf2..55c44056a 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Constant.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Constant.java
@@ -17,7 +17,7 @@
 
 package org.apache.commons.math.analysis.function;
 
-import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 
 /**
  * Constant function.
@@ -25,7 +25,7 @@ import org.apache.commons.math.analysis.UnivariateRealFunction;
  * @version $Id$
  * @since 3.0
  */
-public class Constant implements UnivariateRealFunction {
+public class Constant implements DifferentiableUnivariateRealFunction {
     /** Constant. */
     private final double c;
 
@@ -40,4 +40,9 @@ public class Constant implements UnivariateRealFunction {
     public double value(double x) {
         return c;
     }
+
+    /** {@inheritDoc} */
+    public DifferentiableUnivariateRealFunction derivative() {
+        return new Constant(0);
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Cos.java b/src/main/java/org/apache/commons/math/analysis/function/Cos.java
index 4c24c6bce..9b527ba2c 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Cos.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Cos.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Cos implements UnivariateRealFunction {
+public class Cos implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.cos(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return -FastMath.sin(x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Cosh.java b/src/main/java/org/apache/commons/math/analysis/function/Cosh.java
index a4edc8ced..8db168bfe 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Cosh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Cosh.java
@@ -17,7 +17,7 @@
 
 package org.apache.commons.math.analysis.function;
 
-import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +26,14 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Cosh implements UnivariateRealFunction {
+public class Cosh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.cosh(x);
     }
+
+    /** {@inheritDoc} */
+    public DifferentiableUnivariateRealFunction derivative() {
+        return new Sinh();
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Exp.java b/src/main/java/org/apache/commons/math/analysis/function/Exp.java
index 5ba7d29c5..ce3144c90 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Exp.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Exp.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Exp implements UnivariateRealFunction {
+public class Exp implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.exp(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return FastMath.exp(x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Expm1.java b/src/main/java/org/apache/commons/math/analysis/function/Expm1.java
index 644ce1206..567c986e3 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Expm1.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Expm1.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Expm1 implements UnivariateRealFunction {
+public class Expm1 implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.expm1(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return FastMath.exp(x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Identity.java b/src/main/java/org/apache/commons/math/analysis/function/Identity.java
index c1640a045..994492a5c 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Identity.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Identity.java
@@ -17,7 +17,7 @@
 
 package org.apache.commons.math.analysis.function;
 
-import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 
 /**
  * Identity function.
@@ -25,9 +25,14 @@ import org.apache.commons.math.analysis.UnivariateRealFunction;
  * @version $Id$
  * @since 3.0
  */
-public class Identity implements UnivariateRealFunction {
+public class Identity implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return x;
     }
+
+    /** {@inheritDoc} */
+    public DifferentiableUnivariateRealFunction derivative() {
+        return new Constant(1);
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Inverse.java b/src/main/java/org/apache/commons/math/analysis/function/Inverse.java
index 285fa33b9..284f4459b 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Inverse.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Inverse.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 
 /**
  * Inverse function.
@@ -25,9 +26,19 @@ import org.apache.commons.math.analysis.UnivariateRealFunction;
  * @version $Id$
  * @since 3.0
  */
-public class Inverse implements UnivariateRealFunction {
+public class Inverse implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return 1 / x;
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return -1 / (x * x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Log.java b/src/main/java/org/apache/commons/math/analysis/function/Log.java
index 0750f22fe..e81f77590 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Log.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Log.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Log implements UnivariateRealFunction {
+public class Log implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.log(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / x;
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Log1p.java b/src/main/java/org/apache/commons/math/analysis/function/Log1p.java
index 7ec24599c..c85d4882b 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Log1p.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Log1p.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,19 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Log1p implements UnivariateRealFunction {
+public class Log1p implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.log1p(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return 1 / (1 + x);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Power.java b/src/main/java/org/apache/commons/math/analysis/function/Power.java
index 41ee256e7..f5bca1db2 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Power.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Power.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,7 +27,7 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Power implements UnivariateRealFunction {
+public class Power implements DifferentiableUnivariateRealFunction {
     /** Power. */
     private final double p;
 
@@ -41,4 +42,14 @@ public class Power implements UnivariateRealFunction {
     public double value(double x) {
         return FastMath.pow(x, p);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return p * FastMath.pow(x, p - 1);
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Sin.java b/src/main/java/org/apache/commons/math/analysis/function/Sin.java
index a8bd7e3ac..126d7e1d5 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Sin.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Sin.java
@@ -17,7 +17,7 @@
 
 package org.apache.commons.math.analysis.function;
 
-import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +26,14 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Sin implements UnivariateRealFunction {
+public class Sin implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.sin(x);
     }
+
+    /** {@inheritDoc} */
+    public DifferentiableUnivariateRealFunction derivative() {
+        return new Cos();
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Sinh.java b/src/main/java/org/apache/commons/math/analysis/function/Sinh.java
index 8d9090069..be538c3b4 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Sinh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Sinh.java
@@ -17,7 +17,7 @@
 
 package org.apache.commons.math.analysis.function;
 
-import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +26,14 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Sinh implements UnivariateRealFunction {
+public class Sinh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.sinh(x);
     }
+
+    /** {@inheritDoc} */
+    public DifferentiableUnivariateRealFunction derivative() {
+        return new Cosh();
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Tan.java b/src/main/java/org/apache/commons/math/analysis/function/Tan.java
index 31f7fa211..5cf535130 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Tan.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Tan.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,20 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Tan implements UnivariateRealFunction {
+public class Tan implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.tan(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                final double tanX = FastMath.tan(x);
+                return 1 + tanX * tanX;
+            }
+        };
+    }
 }
diff --git a/src/main/java/org/apache/commons/math/analysis/function/Tanh.java b/src/main/java/org/apache/commons/math/analysis/function/Tanh.java
index 165ed2e3d..524812d9e 100644
--- a/src/main/java/org/apache/commons/math/analysis/function/Tanh.java
+++ b/src/main/java/org/apache/commons/math/analysis/function/Tanh.java
@@ -18,6 +18,7 @@
 package org.apache.commons.math.analysis.function;
 
 import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
@@ -26,9 +27,20 @@ import org.apache.commons.math.util.FastMath;
  * @version $Id$
  * @since 3.0
  */
-public class Tanh implements UnivariateRealFunction {
+public class Tanh implements DifferentiableUnivariateRealFunction {
     /** {@inheritDoc} */
     public double value(double x) {
         return FastMath.tanh(x);
     }
+
+    /** {@inheritDoc} */
+    public UnivariateRealFunction derivative() {
+        return new UnivariateRealFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                final double tanhX = FastMath.tanh(x);
+                return 1 - tanhX * tanhX;
+            }
+        };
+    }
 }