the use of while loop when it comes to files and strings (C language)

I am recently trying to write a code in which the program will show the derivative of a function using the product rule. The function can be either x^n, sin(ax) or cos(ax). I have made local functions, such as

void derivcc (){
double a, b;
fscanf(f,"cos(%lf*x)*cos(%lf*x)",&a, &b);
if (a<0 && b<0) 
printf("%lfsin(%lf*x)*cos(%lf*x)+%lfsin(%lf*x)*cos(%lf*x)\n", -a,a,b,-b,b,a);

else if (a<0 && b>0) 
printf("%lfsin(%lf*x)*cos(%lf*x)-%lfsin(%lf*x)*cos(%lf*x)\n", -a,a,b,b,b,a);

else if (a>0 && b<0) 
printf("-%lfsin(%lf*x)*cos(%lf*x)+%lfsin(%lf*x)*cos(%lf*x)\n", a,a,b,-b,b,a);

else printf("-%lfsin(%lf*x)*cos(%lf*x)-%lfsin(%lf*x)*cos(%lf*x)\n", 
a,a,b,b,b,a);}

However, the issue that I am having is in the main function. I want to know how should I address the while loop, so the local functions can work. Here is the main:

int main(void)
{
FILE * f;
char lines[50];
f=fopen("function.txt", "r");
if (f == NULL)
    {
        printf("Error with opening the file!/n");
        exit (1);
    }
int c;
fgets(lines, sizeof(lines), f); 
char sin[]="sin";
char cos[]="cos";
char x[]="x^";
char *checkc, *checks, *checkx;
checkc = strstr(lines,cos);
checks = strstr(lines,sin);
checkx = strstr(lines, x);
double a,b;


while((c = getc(f)) != EOF) 
{
    if (checks == NULL)
    {
        if (checkc == NULL)
            {
                derivxx();
            }
        else 
            {
                if (checkx==NULL) derivcc();
                else 
                {
                if (lines[0] == cos[0]) derivcx(); 
                else derivxc();
                }
            }
    }
    else 
    {
        if (checkc == NULL && checkx == NULL)
            {
                derivss();
            }
        else 
            {
                if (checkc == NULL && checkx != NULL)/
                {   
                    if (lines[0]==sin[0]) derivsx();
                    else derivxs(); 
                }
                else if (lines[0]==sin[0]) derivsc();
                    else derivcs();
            }
    }
}
fclose(f);