Function to differentiate a polynomial in C++ - c++

Question

I've been trying to get this solved but without luck.
All I want to do is to differentiate a polynomial like P(x) = 3x^3 + 2x^2 + 4x + 5
At the end of the code, the program should evaluate this function and gives me just the answer.
The derivative of P(x) is P'(x) = 3*3x^2 + 2*2x + 4*1. If x = 1, the answer is 17.
I just don't get that answer no matter how I alter my loop.
/*
x: value of x in the polynomial
c: array of coefficients
n: number of coefficients
*/
double derivePolynomial(double x, double c[], int n) {
double result = 0;
double p = 1;
int counter = 1;
for(int i=n-1; i>=0; i--) //backward loop
{
result = result + c[i]*p*counter;
counter++; // number of power
p = p*x;
}
return result;
}
//Output in main() looks like this
double x=1.5;
double coeffs[4]={3,2.2,-1,0.5};
int numCoeffs=4;
cout << " = " << derivePolynomial(x,coeffs,numCoeffs) << endl;

Answer 1

The derivative of x ^ n is n * x ^ (n - 1), but you are calculating something completely different.
double der(double x, double c[], int n)
{
double d = 0;
for (int i = 0; i < n; i++)
d += pow(x, i) * c[i];
return d;
}
This would work, assuming that your polinomial is in the form c0 + c1x + c2x ^ 2 + ...
Demonstration, with another function that does the derivation as well.
Edit: alternative solution avoiding the use of the pow() function, with simple summation and repeated multiplication:
double der2(double x, double c[], int n)
{
double d = 0;
for (int i = 0; i < n - 1; i++) {
d *= x;
d += (n - i - 1) * c[i];
}
return d;
}
This works too. Note that the functions that take the iterative approach (those which don't use pow()) expect their arguments (the coefficients) in reverse order.

Answer 2

You need to reverse the direction of the loop. Start at 0 and go to n.
At the moment when you compute the partial sum for the n-th power p is 1. For the last one x^0 you your p will contain x^n-1 th power.
double derivePolynomial(double x, double c[], int n) {
double result = 0;
double p = 1;
int counter = 1;
for(int i=1; i<n; i++) //start with 1 because the first element is constant.
{
result = result + c[i]*p*counter;
counter++; // number of power
p = p*x;
}
return result;
}
double x=1;
double coeffs[4]={5,4,2,3};
int numCoeffs=4;
cout << " = " << derivePolynomial(x,coeffs,numCoeffs) << endl;