>>634
f(x+y)-f(x-y)=2f(-x)siny
{f(x+y)-f(x)}/y + {f(x-y)-f(x)}/(-y) = 2f(-x)(siny)/y
y→ 0 とすれば
f '(x) + f '(x) = 2f(-x)
f '(x) = f(-x)