西安毛子科技大学函数的求导法则XIDIANUNIVERSITAy证：y=f(u)在点u可导，故 limf'(u).Au-0uAy=f(u)+α(当△u→0 时 α→0)小.AuAy= f'(u)Au+αu..AuAuAy故有(△x # 0)f'(u)+αAxAxAx意dyAyAuulimAu(ulimO= f'(u)g'(x) + lim αdx厂Ax-0Dx?0△xAx△AxAx= f'(u)g'(x)u=g(x）连续，故Ax→0u→0故α→0函数的求导法则 0 lim D ? x 轾 = 犏 臌 0 d lim d x y y x x  →   =  证 故 0 lim ( ) u y f u  → u  =     =  +  y f u u u ( )  故有 = f u g x   ( ) ( ) ( ) ( 0) y u u f u x x x x     = +       0 + lim u u x   →   = f u g x   ( ) ( ) u g x x u =  →  → → ( ) , 0, 0, 0 连续 故 故 y f u = ( ) 在点 u 可导, ( ) y f u u    = +   （当 时 )