#362 - Differentiation of x^x returns wrong expression

sys27 · Oct 6, 2020 · d4e6363 · d4e6363
1 parent 7b06ed2
commit d4e6363
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Showing 2 changed files with 65 additions and 8 deletions.
diff --git a/xFunc.Maths/Analyzers/Differentiator.cs b/xFunc.Maths/Analyzers/Differentiator.cs
@@ -302,10 +302,17 @@ public override IExpression Analyze(Number exp)
         /// </returns>
         public override IExpression Analyze(Pow exp)
         {
-            if (!Helpers.HasVariable(exp, Variable))
-                return new Number(0);
+            var hasVariableInLeft = Helpers.HasVariable(exp.Left, Variable);
+            var hasVariableInRight = Helpers.HasVariable(exp.Right, Variable);
 
-            if (Helpers.HasVariable(exp.Left, Variable))
+            if (hasVariableInLeft && hasVariableInRight)
+            {
+                return new Mul(
+                        exp,
+                        Analyze(new Mul(exp.Right, new Ln(Variable))));
+            }
+
+            if (hasVariableInLeft)
             {
                 var sub = new Sub(exp.Right.Clone(), new Number(1));
                 var inv = new Pow(exp.Left.Clone(), sub);
@@ -315,12 +322,16 @@ public override IExpression Analyze(Pow exp)
                 return mul2;
             }
 
-            // if (Helpers.HasVar(exp.Right, variable))
-            var ln = new Ln(exp.Left.Clone());
-            var mul3 = new Mul(ln, exp.Clone());
-            var mul4 = new Mul(mul3, exp.Right.Clone().Analyze(this));
+            if (hasVariableInRight)
+            {
+                var ln = new Ln(exp.Left.Clone());
+                var mul3 = new Mul(ln, exp.Clone());
+                var mul4 = new Mul(mul3, exp.Right.Clone().Analyze(this));
 
-            return mul4;
+                return mul4;
+            }
+
+            return new Number(0);
         }
 
         /// <summary>

diff --git a/xFunc.Tests/Analyzers/DifferentiatorTest.cs b/xFunc.Tests/Analyzers/DifferentiatorTest.cs
@@ -729,6 +729,52 @@ public void PowDerivativeTest4()
             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(new Number(1), new Ln(Variable.X)),
+                    new Mul(Variable.X, new Div(new Number(1), Variable.X)))
+            );
+
+            Assert.Equal(expected, result);
+        }
+
+        [Fact(DisplayName = "x ^ 2x")]
+        public void PowXby2X()
+        {
+            var exp = new Pow(Variable.X, new Mul(new Number(2), Variable.X));
+            var result = Differentiate(exp);
+            var expected = new Mul(
+                new Pow(Variable.X, new Mul(new Number(2), Variable.X)),
+                new Add(
+                    new Mul(new Mul(new Number(2), new Number(1)), new Ln(Variable.X)),
+                    new Mul(new Mul(new Number(2), Variable.X), new Div(new Number(1), 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), new Number(1)), new Ln(Variable.X)),
+                    new Mul(new Sin(Variable.X), new Div(new Number(1), Variable.X))
+                )
+            );
+
+            Assert.Equal(expected, result);
+        }
+
         [Fact]
         public void PowPartialDerivativeTest1()
         {