Data update

Task/Arithmetic-derivative/Sidef/arithmetic-derivative-2.sidef

@@ -0,0 +1,26 @@
+subset Integer  < Number   { .is_int   }
+subset Positive < Integer  { .is_pos   }
+subset Negative < Integer  { .is_neg   }
+subset Prime    < Positive { .is_prime }
+
+func arithmetic_derivative((0)) { 0 }
+func arithmetic_derivative((1)) { 0 }
+
+func arithmetic_derivative(Prime _) { 1 }
+
+func arithmetic_derivative(Negative n) {
+    -arithmetic_derivative(-n)
+}
+
+func arithmetic_derivative(Positive n) is cached {
+
+    var a = n.factor.rand
+    var b = n/a
+
+    arithmetic_derivative(a)*b + a*arithmetic_derivative(b)
+}
+
+func arithmetic_derivative(Number n) {
+    var (a, b) = n.nude
+    (arithmetic_derivative(a)*b - arithmetic_derivative(b)*a) / b**2
+}