dual_class.py

class Dual:
    def __init__(self, value=0., derivative=0.):
        self.value = value
        self.derivative = derivative

    def __add__(self, other):
        return Dual(self.value + other.value, self.derivative + other.derivative)

    def __mul__(self, other):
        return Dual(self.value * other.value, self.value*other.derivative + self.derivative * other.value)

    def __pow__(self, other):
        if self.value > 0.:
            return Dual(self.value**other.value, self.derivative * other.value * self.value**(other.value-1) + other.derivative * self.value**other.value * math.log(self.value))
        else:
            return Dual(self.value**other.value, self.derivative * other.value * self.value**(other.value-1))

    def __truediv__(self, other):
        return self * other**(-1.)