Complete the function that calculates the derivative of a polynomial. A polynomial is an expression like: 3x^(4) - 2x^(2) + x - 10

### How to calculate the derivative:

* Take the exponent and multiply it with the coefficient
* Reduce the exponent by 1

For example: 3x^(4) --> (4*3)x^((4-1)) = 12x^(3)

### Good to know:

* The derivative of a constant is 0 (e.g. 100 --> 0)
* Anything to the 0th exponent equals 1 (e.g. x^(0) = 1)
* The derivative of the sum of two function is the sum of the derivatives

Notes:
* The exponentiation is marked with "^"
* Exponents are always integers and >= 0
* Exponents are written only if > 1
* There are no spaces around the operators
* Leading "+" signs are omitted

See the examples below.

## Examples
```python
derivative("-100")      = "0"
derivative("4x+1")      = "4"      # = 4x^0 + 0
derivative("-x^2+3x+4") = "-2x+3"  # = -2x^1 + 3x^0 + 0
```

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import re\nnomial = re.compile(r\'(?P<sign>[\\+-]?)(?P<coef>[0-9]*)(?P<x>[a-z]?)\\^?(?P<exp>[0-9]*)\')\n\ndef derive(eq):\n    if not eq: return \'\'\n    m = nomial.match(eq)\n    c = int(m.group(\'coef\') or \'1\')\n    exp = int(m.group(\'exp\') or \'1\')\n    if not m.group(\'x\'): r = "" \n    elif not m.group(\'exp\'): r = m.group(\'sign\')+ str(c)\n    elif m.group(\'exp\') == \'2\': r = m.group(\'sign\')+str(c * 2)+m.group(\'x\')\n    else: r = m.group(\'sign\')+str(c*exp)+m.group(\'x\')+\'^\'+str(exp-1)\n    return r + derive(eq[m.end():])\n\ndef derivative(eq):\n    return derive(eq) or \'0\''
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'derivative'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 7591