public override Operand Differentiate()
{
// (f(x))^b where b is a natural number even.
// The general power rule but combined with the
// chain rule. b * (f(x))^(b - 1) * f'(x)
// b
Operand power = RightSuccessor.Copy();
// b - 1
Integer newPower = new Integer(Convert.ToDouble(power.Data) - 1);
// f(x)^(b - 1)
Power onePowerLess = new Power();
onePowerLess.LeftSuccessor = LeftSuccessor.Copy();
onePowerLess.RightSuccessor = newPower;
// f'
Operand derivativeOfF = LeftSuccessor.Differentiate();
// b * f(x)^(b - 1)
Multiplication intermediaryResult = new Multiplication();
intermediaryResult.LeftSuccessor = power;
intermediaryResult.RightSuccessor = onePowerLess;
// (b * f(x)^(b - 1)) * f'
Multiplication derivative = new Multiplication();
derivative.LeftSuccessor = intermediaryResult;
derivative.RightSuccessor = derivativeOfF;
return(derivative);
}
public override Operand Copy()
{
Multiplication copy = new Multiplication();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
public override Operand Copy()
{
Power copy = new Power();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
public override Operand Copy()
{
Addition copy = new Addition();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
public override Proposition Copy()
{
Nand copy = new Nand();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
public override Proposition Copy()
{
BiImplication copy = new BiImplication();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
public override Proposition Copy()
{
Conjunction copy = new Conjunction();
copy.LeftSuccessor = LeftSuccessor.Copy();
copy.RightSuccessor = RightSuccessor.Copy();
return(copy);
}
/// <summary>
/// Applies the product rule to the sub trees.
/// (f * g)' = f * g' + f' * g
///
/// The method differentiates the appropriate sub trees and
/// eventually returns a single Operand object (in this case
/// an addition operator object) holding both an original
/// expression sub tree as well as a differentiated sub tree.
/// </summary>
/// <returns>
/// An operator object, representing the applied product rule.
/// </returns>
public override Operand Differentiate()
{
// Create and assign fg'
Multiplication newLeftExpression = new Multiplication();
newLeftExpression.LeftSuccessor = LeftSuccessor.Copy();
newLeftExpression.RightSuccessor = RightSuccessor.Differentiate();
// Create and assign f'g
Multiplication newRightExpression = new Multiplication();
newRightExpression.LeftSuccessor = LeftSuccessor.Differentiate();
newRightExpression.RightSuccessor = RightSuccessor.Copy();
// Create and assign fg' + f'g
Addition derivative = new Addition();
derivative.LeftSuccessor = newLeftExpression;
derivative.RightSuccessor = newRightExpression;
return(derivative);
}