Fix computing derivative of negated exponential expressions

src/rules/derivatives.py

@@ -208,7 +208,7 @@ def variable_root(root, args):
     """
     x, n = root[0]
 
-    return n * x ** (n - 1)
+    return (n).negate(root[0].negated) * x ** (n - 1)
 
 
 MESSAGES[variable_root] = \
@@ -225,9 +225,9 @@ def variable_exponent(root, args):
     g, x = root[0]
 
     if g == E:
-        return g ** x
+        return (g ** x).negate(root[0].negated)
 
-    return g ** x * ln(g)
+    return (g ** x).negate(root[0].negated) * ln(g)
 
 
 MESSAGES[variable_exponent] = \

tests/test_rules_derivatives.py

@@ -138,6 +138,11 @@ class TestRulesDerivatives(RulesTestCase):
         x, n = root[0]
         self.assertEqual(variable_root(root, ()), n * x ** (n - 1))
 
+    def test_variable_root_with_negation(self):
+        root = tree('d/dx -x ^ 2')
+        x, n = root[0]
+        self.assertEqual(variable_root(root, ()), -n * x ** (n - 1))
+
     def test_variable_exponent(self):
         root = tree('d/dx 2 ^ x')
         g, x = root[0]
@@ -147,6 +152,10 @@ class TestRulesDerivatives(RulesTestCase):
         e, x = root[0]
         self.assertEqual(variable_exponent(root, ()), e ** x)
 
+        root = tree('d/dx -e ^ x')
+        e, x = root[0]
+        self.assertEqual(variable_exponent(root, ()), -e ** x)
+
     def test_chain_rule(self):
         root = tree('(2 ^ x ^ 3)\'')
         l2, x3 = root[0]