The n functions f_1(x), f_2(x), ..., f_n(x) are linearly dependent if, for some c_1, c_2, ..., c_n element R not all zero, sum_(i = 1)^n c_i f_i(x) = 0 for all x in some interval I. If the functions are not linearly dependent, they are said to be linearly independent. Now, if the functions and in C^(n - 1) (the space of functions with n - 1 continuous derivatives), we can differentiate (-1) up to n - 1 times.