classes the multiplication of two polynomials is slightly more complex than their additionso it is worth writing down the mathematics before implementing the __mul__ method the formula looks like ci xi dj xj ci dj xi+ = = = = whichin our list representationmeans that the coefficient corresponding to the power is ci dj the list of coefficients for the resulting polynomial should have length and an element [kshould be the sum of all products [ ]* [jfor which the implementation of the method could look like class polynomialdef __mul__(selfother) len(self coeff len(other coeff coeff [ ]*( + + or zeros( + + for in range( + )for in range( + )coeff[ + +self coeff[ ]*other coeff[jreturn polynomial(coeffjust as the __add__ method__mul__ takes one argument in addition to selfand returns new polynomial instance turning now to the differentiate methodthe rule for differentiating general polynomial is ci ici xi- dx = = thereforeif is the list of coefficientsthe derivative has list of coefficients dcwhere dc[ - * [ifor from one to the largest index in note that dc will have one element less than csince differentiating polynomial reduces the order by one the full implementation of the differentiate method could look like the followingclass polynomialdef differentiate(self)change self for in range( len(self coeff))self coeff[ - *self coeff[idel self coeff[- def derivative(self)return new polynomial dpdx polynomial(self coeff[:]copy dpdx differentiate(return dpdx