public override Node ReturnDerivative(double x)
{
if (leftNode is NumberNode && rightNode is NumberNode)
{
return(new NaturalNumberNode(0));
}
else if (leftNode is VariableNode && (rightNode is NaturalNumberNode || rightNode is RationalNumberNode))
{
RationalNumberNode rationalNumberNodeA = new RationalNumberNode(rightNode.Calculate(x));
RationalNumberNode rationalNumberNodeB = new RationalNumberNode(rightNode.Calculate(x) - 1);
CaretSign caretSign = new CaretSign(leftNode.Copy(), rationalNumberNodeB);
MultiplicationSign multiplicationSign = new MultiplicationSign(rationalNumberNodeA, caretSign);
return(multiplicationSign);
}
else if (leftNode is NumberNode)
{
LogarithmFunction logarithmFunction = new LogarithmFunction(leftNode.Copy());
CaretSign caretSign = new CaretSign(leftNode.Copy(), rightNode.Copy());
MultiplicationSign multiplicationSignA = new MultiplicationSign(logarithmFunction, caretSign);
MultiplicationSign multiplicationSignB = new MultiplicationSign(multiplicationSignA, caretSign.rightNode.ReturnDerivative(x));
return(multiplicationSignB);
}
else
{
MinusSign minusSign = new MinusSign(rightNode.Copy(), new NaturalNumberNode(1));
CaretSign caretSign = new CaretSign(leftNode.Copy(), minusSign);
MultiplicationSign multiplicationSignA = new MultiplicationSign(rightNode.Copy(), caretSign);
MultiplicationSign multiplicationSignB = new MultiplicationSign(multiplicationSignA, leftNode.ReturnDerivative(x));
return(multiplicationSignB);
}
}
public double ReturnNewtonMaclaurinSeries(double x, int order)
{
if (order == 0)
{
return(Calculate(0));
}
if (order == 1)
{
return(ReturnNewtonDerivative(0) * x + Calculate(0));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
RationalNumberNode f0 = new RationalNumberNode(CalculatePolynomialDerivative(0, order));
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, f0);
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(divisionSign.Calculate(x) + ReturnNewtonMaclaurinSeries(x, order - 1));
}