In this question, we represent a polynomial (of degree n)a0 + a1x + a2x2 + · · · + anxnas a list of its coefficients pol=[a0, a1, a2, . . . , an]. For instance, 6 − 5x + x3 is representedas [6, −5, 0, 1](a)[1] Write a function differentiate polynomial(pol) which computes the derivativeof pol and represents it again as a list of coefficients.(b)[1] Write a function integrate polynomial(pol) which computes the antiderivativeof pol and represents it again as a list of coefficients (you can assume that the integrationconstant is zero).You are not allowed to use any modules/packages for this question; instead, write yourown code.THE END3

Sure, here is the Python code for the functions you asked for:

(a) Differentiate a polynomial:

def differentiate_polynomial(pol):
    return [i*a for i, a in enumerate(pol)][1:]

(b) Integrate a polynomial:

def integrate_polynomial(pol):
    return [a/(i+1) for i, a in enumerate(pol)] + [0]

In the differentiate_polynomial function, we use the enumerate function to get both the index and the value of each element in the list. The index represents the power of x in the polynomial, and when we differentiate, we bring down the power of x and subtract one from the power. We start from the second element (index 1) because the derivative of a constant (a0) is zero.

In the integrate_polynomial function, we do the opposite. We divide each coefficient by the power of x plus one, and add a zero at the end of the list to represent the integration constant.