given that { f(x), f' (x)..., f^n (x)} is a basis for Pn,

then a_0 f(x)+ a_1 f'(x)+...a_n f^n (x)=0 , hw can you tell that the leading coefficient is a_0 a_n and that

for a_1 f'(x)+...a_n f^n (x)=0 where a_0 f(x)=0 then the leading coefficient is 2a_1 a_n?