/// <summary>
/// (f + g)' = f' + g'
/// Meaning we differentiate both the left and right sub tree first
/// and return an addition operator with the differentiated sub trees
/// as it's successors
/// </summary>
/// <returns>
/// An addition operator object with both left
/// and right successor differentiated.
/// </returns>
public override Operand Differentiate()
{
Addition derivative = new Addition();
derivative.LeftSuccessor = LeftSuccessor.Differentiate();
derivative.RightSuccessor = RightSuccessor.Differentiate();
return(derivative);
}
/// <summary>
/// (f - g)' = f'- g'
/// Meaning we differentiate both the left and right sub tree first
/// and return a subtraction operator with the differentiated sub trees
/// as it's successors
/// </summary>
/// <returns>
/// A subtraction operator object with both left
/// and right successor differentiated.
/// </returns>
public override Operand Differentiate()
{
Operand leftDerivative = LeftSuccessor.Differentiate();
Operand rightDerivative = RightSuccessor.Differentiate();
Subtraction derivative = new Subtraction();
derivative.LeftSuccessor = leftDerivative;
derivative.RightSuccessor = rightDerivative;
return(derivative);
}
/// <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);
}