"please follow all the instructions before attempting this question, other wise I will dislike you"

(1) please write in python.

(2) **this is very important*** please attempt all functions** (here 2 functions are given i.e

a) mul_coeff(n):

b) diff_coeff(n):

(3) please provide screenshot of test run of your code.

(4) ****this is also very important **** please explain all the steps of your algorithm in comments.

(5) do not copy from chegg or any other internet resources.

(you can take more than 2 hours ,i don't mind but algorithm should be correct)

if you left any part , I will dislike you, so please carefully attend the question.

Question 1 (please attempt both parts) Suppose we have two functions cos(x)and In(1+x) represented as Taylor series, cos(x) = 1 - + +... In(1 + x) = x - + ... *****Let f(x) =cos(x) and g(x) =In(1+x)**** Write the following functions in python : 1) mul_coeff(n): returns the coefficient of x^n in the Taylor series of f (x)*g(x) (Hint--First try this out by hand, then write the code after having figured out the pattern.) >>>mul_coeff(2) -0.5 2) diff_coeff(n): returns the coefficient of x^n in the Taylor series of d.f(x) dx (Hint: here you have to differentiate f(x) and then find coefficient of x^n >>>diff_coeff(3) 0.1666666667