I found this problem in online book of Christian Hill here
go through the problem and understand what is has to say, also Christian Hill is one of god authors in computational physics field
if incase link has some problem, here i rewrite the problem as it is given in the book
'''
Using a list to represent a polynomial
Question Q2.4.2
A list could be used as a simple representation of a polynomial, P(x),
with the items as the coefficients of the successive powers of x,
and their indexes as the powers themselves.
Thus, the polynomial P(x)=4+5x+2x3 would be represented by the list [4, 5, 0, 2].
Why does the following attempt to differentiate a polynomial fail to produce the correct answer?
'''
######################################
P = [4, 5, 0, 2]
dPdx = []
for i, c in enumerate(P[1:]):
dPdx.append(i*c)
dPdx
[0, 0, 4] # wrong!
######################################
'''
How can this code be fixed?
'''
My version/modification to this problem is
Write a program/function that returns a string that is
output of differentiation of input string
Input string has to be polynomial only in X
AND
increasing form of power only
For example
Input : "5+4x+3x**2+2x**3"
Output : "4+6x+6x**2"
Also if polynomial have some step missing for example
Input is 5x³ + 4x + 2
Then also input string has to be
2+4x+0x**2+5x**3
"WARNING" :: Do not use any library, only do it with
help of lists strings dictionaries and pure logic
NOTE :: Program , when returning, should not return x**1 in string,
only coefficient with x should be returned,
for example;
2+3x**1+4x**2+5X**3 # WRONG
2+3x+4x**2+5X**3 # RIGHT
SIMILAR PROBLEM / SUB PROBLEM STATEMENT :: similarly create function/program for integration