# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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
```

## tags:

Mathematical maths-polynomial Mathematical