/*
** Notation:
**   f(x) is the original function.
**   f1(x) is the first derivative of the function.
**   f2(x) is the second derivative of the function.
**   f3(x) is the third derivative of the function.
**   f4(x) is the fourth derivative of the function.
**   f5(x) is the fifth derivative of the function.
**   f6(x) is the sixth derivative of the function.
**   f7(x) is the seventh derivative of the function.
**   f8(x) is the eighth derivative of the function.
**   f9(x) is the ninth derivative of the function.
**   f10(x) is the tenth derivative of the function.
*/

typedef long double number;

typedef number (*ftype) (number);

extern number al1(ftype, ftype, number, number);
extern number bl1(ftype, ftype, ftype, number, number);
extern number al2(ftype, ftype, ftype, number, number);
extern number bl2(ftype, ftype, ftype, ftype, number, number);
extern number al3(ftype, ftype, ftype, ftype, number, number);
extern number bl3(ftype, ftype, ftype, ftype, ftype, number, number);
extern number al4(ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl4(ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number al5(ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl5(ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number al6(ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl6(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number al7(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl7(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number al8(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl8(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number al9(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);
extern number bl9(ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, ftype, number, number);