differentiate-a-polynomial

def split_terms(equation):
    split_terms = []
    chr_buffer = []
    for chr in equation:
        if chr in ["+", "-"]:
            if len(chr_buffer) > 0:
                split_terms.append(''.join(chr_buffer))
            chr_buffer = [chr]
        else:
            chr_buffer.append(chr)
    if len(chr_buffer) > 0:
        split_terms.append(''.join(chr_buffer))
    return split_terms
    
def _coeficient(comp):
    #print(comp)
    if comp == '':
        return 1
    if comp == '-':
        return -1   
    if comp == '+':
        return 1        
    return int(comp)

    
def differentiate(equation, point):
    terms = split_terms(equation)
    #print(equation)
    #print(terms)
    #print(point)
    new_terms = []
    for term in terms:
        comp = term.split('x')
        # constant value
        if len(comp) == 1:
            continue
        
        coeficient = _coeficient(comp[0])
        caret_pos = comp[1].find('^')
        
        # 1st degree
        if caret_pos == -1:
            new_terms.append(coeficient)    
            continue
        
        # 2nd or greater degree
        caret_parts = comp[1].split('^')
        exponent = int(caret_parts[1])
        new_terms.append(exponent * coeficient * (point ** (exponent - 1)))
    
    #print(new_terms)
    return sum(new_terms)