若函数f(x)在x=a处的导数为A,求limh趋向于0f(a+4h)-f(a+5h)/h的值

f'(x) = lim(h->0) [f(x+h) -f(x) ] /h
f'(a) =lim(h->0) [f(a+h) -f(a) ] /h
lim(h->0) [f(a+4h) -f(a+5h)] /h
=lim(h->0) [ (f(a+4h) -f(a)) - ( f(a+5h)-f(a)) ] /h
= lim(h->0) [f(a+4h)-f(a)] /h - lim(h->0) [f(a+5h)-f(a)]/h
= 4lim(h->0) [f(a+4h)-f(a)] /(4h) - 5lim(h->0) [f(a+5h)-f(a)]/(5h)
=4f'(a) -5f'(a)
=-A