KEY ITEMS: Key items are marked in red. Failure to include or complete key items will incur additional deductions as noted beside the item.

Problem: As usual, Wario is concerned about nothing other than acquiring more money. In order to maximize profits, Wario needs to use calculus to create derivatives for analysis. Unfortunately, Wario never took calculus; there wasnt much need of it in the Mushroom Kingdom. So, Wario is calling on you to help him by creating a program to create derivatives.

Pseudocode: Your pseudocode should describe the following items

• Main.cpp
  • Detail the step-by-step logic of the mainfunction
  • List other functions you plan tocreate
    • Determine the parameters
    • Determine the return type
    • Detail the step-by-step logic that the function will perform
• You do not need to write any pseudocode for any of the class functions

Details

• This project must use two classes created in review homework #7
  • Linked Listclass
  • Nodeclass
• Linked Listclass
  • Variables
    • Head node pointer
  • Functions
    • Default constructor
    • Overloaded Constructor
      • Make copy of list passed in
    • Destructor
      • Delete thelist
    • Accessors andmutators
    • Overloaded operators created in review homework #8
      • Overloaded []
        • Return the node at the givenindex
      • Overloaded << operator
        • Display the linkedlist
        • Use [] notation to treat the linked list like an array
        • See output format below
      • Overloaded ++ operator
        • Prefix notation only
        • Add node to head of linkedlist
    • Sort
      • Sort the linked list in descending order by exponent
• Nodeclass
  • Variables
    • Outer coefficient
    • Innercoefficient
    • (optional) numerator and denominator variables if doing extra creditportion
    • Exponent
    • Trigidentifier
    • Nodepointer
  • Functions
    • Defaultconstructor
    • Overloadedconstructor
    • Accessors andmutators
    • Overloaded << operator created in review homework #8
      • Display a singlenode
      • See output format below
• All nodes will be dynamicallycreated
  • There should only be enough nodes to hold data for the current expression
  • You will have to consider a way to reuse the linked list for the next expression
• All input will be read from afile
• Each term in the expression will be stored into a node and added into the linkedlist
• Each line in the file will be a mathematical function that can be derived
• The number of lines in the file is unknown
• Each calculated derivative will be written to afile

User Interface: There will be no user interface for this program

Input: All input will be read from a file named functions.txt. Each line in the file will be a mathematical function with the following parameters:

• Consist of polynomial terms the highest degree will be10
• May also contain trigfunctions
• Exponents will be represented by the ^ character.
• Exponents may be positive ornegative
• Do not assume that the expression will be in order from highest to lowest exponent.
• All coefficients will beintegers.
• The absence of a coefficient should be interpreted as a coefficient of1
• Trigonometric functions may havecoefficients
• The variable will always be x.
• There will be spaces around the operators between terms
• If a trig function is used, there will be a space between the trig function and the coefficient of x
• ExampleInput:
  • 3x^2 + 2x + 1
  • x^-2 + 3x + 4
  • 4x x^3
  • 3sin x + cosx
  • 1 cos4x
  • 3x^4 6x^2 + tan 10x

Output: All output will be written to a file.

• The file will be namedtxt.
• Each derivative will be written on a separate line.
• Use the ^ character to represent exponents.
• The terms of the derivative must be ordered from highest to lowest exponent
  • Trig functions should be listed at the end in the order they were encountered in the original expression
• The format of the output for each term will be the same as the input format
• Do not use double operators
  • Invalid format: 2x^2 +-3x

EXTRA CREDIT: Add to your program to derive functions with fractional coefficients (potential 25 extra points for this project)

• Fractional coefficients will be enclosed within parentheses (for both input andoutput)
• Each coefficient in the derivative should be simplified as much as possible
• Fractional coefficients with a denominator of 1 after derivation will be written as a whole number without parentheses
• ExampleInput
  • x (1/4)sin4x
  • (3/5)x^5 2x^3 10cos10x