高等数学_例题解-5

例5求函数(x)= Flog(a>0,a≠1)的导数 fi f(=lim log a(x+h-l0ga-x=lim l log (+h, h->0 h->0 x008( ogae xIn a 即(ogax) xIn a 特殊地(lnx)= 上页 下页

上页 结束 下页 例5 求函数f(x)=loga x (a0 a1)的导数 解 h x h x f x a a h log ( ) log ( ) lim 0 + −  = → log (1 ) 1 lim 0 x h h a h = + → 解 h x a h x h x lim log (1 ) 1 0 = + → x a e x a ln 1 log 1 = =  特殊地 x x 1 (ln ) =  即 x a xa ln 1 即 (log ) =  解 h x h x f x a a h log ( ) log ( ) lim 0 + −  = → log (1 ) 1 lim 0 x h h a h = + → h x a h x h x lim log (1 ) 1 0 = + → x a e x a ln 1 log 1 = =  结束