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Program for Derivative of a Polynomial

Given a polynomial as string and a value. Evaluate polynomial’s derivative for the given value.
Note: The input format is such that there is a whitespace between a term and the ‘+’ symbol

The derivative of p(x) = ax^n is p'(x) = a*n*x^(n-1)

Also, if p(x) = p1(x) + p2(x)
Here p1 and p2 are polynomials too
p'(x) = p1′(x) + p2′(x)

Input : 3x^3 + 4x^2 + 6x^1 + 89x^0
        2             
Output :58 
Explanation : Derivative of given
polynomial is : 9x^2 + 8x^1 + 6
Now put x = 2
9*4 + 8*2 + 6 = 36 + 16 + 6 = 58  
            
Input : 1x^3
        3
Output : 27



We split the input string into tokens and for each term calculate the derivative separately for each term and add them to get the result.

// CPP program to find value of derivative of
// a polynomial.
#include <bits/stdc++.h>
using namespace std;
  
long long derivativeTerm(string pTerm, long long val)
{
    // Get coefficient
    string coeffStr = "";
    int i;
    for (i = 0; pTerm[i] != 'x'; i++)
        coeffStr.push_back(pTerm[i]);
    long long coeff = atol(coeffStr.c_str());
  
    // Get Power (Skip 2 characters for x and ^)
    string powStr = "";
    for (i = i + 2; i != pTerm.size(); i++)
        powStr.push_back(pTerm[i]);
    long long power = atol(powStr.c_str());
  
    // For ax^n, we return a(n-1)x^(n-1)
    return coeff * power * pow(val, power - 1);
}
  
long long derivativeVal(string& poly, int val)
{
    long long ans = 0;
  
    // We use istringstream to get input in tokens
    istringstream is(poly);
  
    string pTerm;
    while (is >> pTerm) {
  
        // If the token is equal to '+' then
        // continue with the string
        if (pTerm == "+")
            continue;
  
        // Otherwise find the derivative of that
        // particular term
        else
            ans = (ans + derivativeTerm(pTerm, val));
    }
    return ans;
}
  
// Driver code
int main()
{
    string str = "4x^3 + 3x^1 + 2x^2";
    int val = 2;
    cout << derivativeVal(str, val);
    return 0;
}

Output:

59

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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