Fix #362 - Differentiation of x^x returns wrong expression

sys27 · Oct 6, 2020 · 02f2b02 · 02f2b02
1 parent fc26c3f
commit 02f2b02
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Showing 2 changed files with 70 additions and 23 deletions.
diff --git a/xFunc.Maths/Analyzers/Differentiator.cs b/xFunc.Maths/Analyzers/Differentiator.cs
@@ -240,27 +240,29 @@ public override IExpression Analyze(Pow exp, DifferentiatorContext context)
         {
             ValidateArguments(exp, context);
 
-            if (Helpers.HasVariable(exp.Left, context.Variable))
-            {
-                return new Mul(
-                    exp.Left.Analyze(this, context),
-                    new Mul(
-                        exp.Right,
-                        new Pow(
-                            exp.Left,
-                            new Sub(exp.Right, Number.One))));
-            }
+            var hasVariableInLeft = Helpers.HasVariable(exp.Left, context.Variable);
+            var hasVariableInRight = Helpers.HasVariable(exp.Right, context.Variable);
 
-            if (Helpers.HasVariable(exp.Right, context.Variable))
+            return (hasVariableInLeft, hasVariableInRight) switch
             {
-                return new Mul(
+                (true, true) =>
                     new Mul(
-                        new Ln(exp.Left),
-                        exp),
-                    exp.Right.Analyze(this, context));
-            }
-
-            return Number.Zero;
+                        exp,
+                        new Mul(exp.Right, new Ln(context.Variable)).Analyze(this, context)),
+                (true, _) =>
+                    new Mul(
+                        exp.Left.Analyze(this, context),
+                        new Mul(
+                            exp.Right,
+                            new Pow(
+                                exp.Left,
+                                new Sub(exp.Right, Number.One)))),
+                (_, true) =>
+                    new Mul(
+                        new Mul(exp, new Ln(exp.Left)),
+                        exp.Right.Analyze(this, context)),
+                _ => Number.Zero,
+            };
         }
 
         /// <inheritdoc />

diff --git a/xFunc.Tests/Analyzers/DifferentiatorTests/DifferentiatorTest.cs b/xFunc.Tests/Analyzers/DifferentiatorTests/DifferentiatorTest.cs
@@ -579,7 +579,7 @@ public void MulPartialDerivativeTest4()
             Assert.Equal(zero, deriv);
         }
 
-        [Fact]
+        [Fact(DisplayName = "x ^ 3")]
         public void PowDerivativeTest1()
         {
             var exp = new Pow(Variable.X, new Number(3));
@@ -592,23 +592,68 @@ public void PowDerivativeTest1()
             Assert.Equal(expected, deriv);
         }
 
-        [Fact]
+        [Fact(DisplayName = "2 ^ (3x)")]
         public void PowDerivativeTest2()
         {
-            // 2 ^ (3x)
             var exp = new Pow(Number.Two, new Mul(new Number(3), Variable.X));
             var deriv = Differentiate(exp);
             var expected = new Mul(
                 new Mul(
-                    new Ln(Number.Two),
-                    new Pow(Number.Two, new Mul(new Number(3), Variable.X))
+                    new Pow(Number.Two, new Mul(new Number(3), Variable.X)),
+                    new Ln(Number.Two)
                 ),
                 new Mul(new Number(3), Number.One)
             );
 
             Assert.Equal(expected, deriv);
         }
 
+        [Fact(DisplayName = "x ^ x")]
+        public void PowXbyX()
+        {
+            var exp = new Pow(Variable.X, Variable.X);
+            var result = Differentiate(exp);
+            var expected = new Mul(
+                new Pow(Variable.X, Variable.X),
+                new Add(
+                    new Mul(Number.One, new Ln(Variable.X)),
+                    new Mul(Variable.X, new Div(Number.One, Variable.X)))
+            );
+
+            Assert.Equal(expected, result);
+        }
+
+        [Fact(DisplayName = "x ^ 2x")]
+        public void PowXby2X()
+        {
+            var exp = new Pow(Variable.X, new Mul(Number.Two, Variable.X));
+            var result = Differentiate(exp);
+            var expected = new Mul(
+                new Pow(Variable.X, new Mul(Number.Two, Variable.X)),
+                new Add(
+                    new Mul(new Mul(Number.Two, Number.One), new Ln(Variable.X)),
+                    new Mul(new Mul(Number.Two, Variable.X), new Div(Number.One, Variable.X)))
+            );
+
+            Assert.Equal(expected, result);
+        }
+
+        [Fact(DisplayName = "x ^ sin(x)")]
+        public void PowXbySinX()
+        {
+            var exp = new Pow(Variable.X, new Sin(Variable.X));
+            var result = Differentiate(exp);
+            var expected = new Mul(
+                new Pow(Variable.X, new Sin(Variable.X)),
+                new Add(
+                    new Mul(new Mul(new Cos(Variable.X), Number.One), new Ln(Variable.X)),
+                    new Mul(new Sin(Variable.X), new Div(Number.One, Variable.X))
+                )
+            );
+
+            Assert.Equal(expected, result);
+        }
+
         [Fact]
         public void PowPartialDerivativeTest1()
         {