-2x^2+2x-3

-2x+sinx-3

-x+sin2x-tanx

Open the file.
While there's lines to read:
   Read a line -
   Seperate it by the operands (+,-,/,*)
   For each part:
     Find the power of x,
     Reduce it by one,
     ...(derivating rules) // no way around, you have to implement each function if you want this to work as others mentioned in the comments.
   Reconnect the parts into a string,
   Add it to a list.
 Print each element of the list.

-2x^2+2x-3     =>  2x^2  2x     3
-2x+sinx-3     =>  2x    sinx   3
-x+sin2x-tanx  =>  x     sin2x  tanx

-2x^2 + 5x + 4sin3x - 3

0 - 2x^2 + 5x + 4sin3x - 3

0      [0x^1]   (derives as) 0, remove it.
2x^2   [2x^2]   (derives as) (2*2)x^(2-1) => 4x^1 => 4x
5x     [5x^1]   (derives as) (5x1)x^(1-1) => 5x^0 => 5
4sin3x [4sin3x] (derives as) 12cos3x
3      [3x^0]   (derives as) 0, remove it and preceding '-'

#define maxlen 50

#define idx         0 //X variable
#define idnumber    1 //number
#define idplus      2 //+ sign
#define idminus     3 //- sign

struct foo
{
    int type[10];//each type can be a number (idnum), +, -, etc.
    int num[10];//if type[i] is number then num[i] identifies that number
    int count;//total number of parts
};

void parse_one_line(struct foo *v, const char *s)
{
    char buf[maxlen];
    memset(buf, 0, maxlen);
    int j = 0;
    //remove white spaces
    for (int i = 0, len = strlen(s); i < len; i++)
    {
        if (s[i] == ' ') continue;
        buf[j] = s[i];
        j++;
    }

    char part[maxlen];
    v->count = 0;
    for (int i = 0, len = strlen(buf); i < len; i++)
    {
        char c = buf[i];
        if (c == 'x')
        {
            v->type[v->count] = idx;
            v->count++;
        }
        else if (c == '+')
        {
            v->type[v->count] = idplus;
            v->count++;
        }
        else if (c == '-')
        {
            v->type[v->count] = idminus;
            v->count++;
        }
        else if (c >= '0' && c <= '9')
        {
            int j = 0;
            memset(part, 0, maxlen);
            for (; i < len; i++)
            {
                c = buf[i];
                if (c >= '0' && c <= '9')
                {
                    part[j] = c;
                    j++;
                }
                else
                {
                    break;
                }
            }
            i--;
            v->num[v->count] = atoi(part);
            v->type[v->count] = idnumber;
            v->count++;
        }
    }
    for (int i = 0; i < v->count; i++)
    {
        switch (v->type[i])
        {
        case idnumber: printf("%d", v->num[i]); break;
        case idx: printf("X"); break;
        case idplus: printf("+"); break;
        case idminus: printf("-"); break;
        default:break;
        }
    }
    printf("n");
}

int main()
{
    struct foo st;
    parse_one_line(&st, "-23x + 2 + 2x - 3");
    return 0;
}