f(x)=lgx f(x+△)=lg(x+△) f'(x)=[f(x+△)-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x) =lg[(x+△)/x]/△ =1/△ *lg[1+△/x] =lg[1+△/x]^(1/△) =lg[1+△/x]^(x/x△) =lg[1+△/x]^[(x/△)*1/x] =1/x*lg[1+△/x]^[(x/△) 当△->0时 [1+△/x]^[(x/△)->e ∴f'(x)=1/x ...
解答一 举报 loga(x)的导数是1/(xlna),其中a为常数f(x)=xlgx的导数就是lgx+x*1/(xln10)=lgx+1/ln10 还可进一步推出=lgx+lne/ln10=lgx+lge=lg(ex) 解析看不懂?免费查看同类题视频解析查看解答 更多答案(1) 相似问题 f(x)' [f(x)]' 导数 f(1/x)=x/(1+x),则f'(x)=? 10^xlgx的...
lgx的导数是1/[xln(10)]。lgx = lnx/ln(10)。(lnx)' = 1/x。(lgx)' = [lnx/ln(10)]' = (lnx)'/ln(10) = (1/x)/ln(10) = 1/[xln(10)]。lg表示以10为底的对数（常用对数），如lg10=1。根据微积分基本定理，对于可导的函数，有：如果函数的导函数在某一区间内恒大于零（...
lgx 怎么求导? 相关知识点: 试题来源: 解析f(x)=lgxf(x+△)=lg(x+△)f'(x)=[f(x+△)-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x) =lg[(x+△)/x]/△ =1/△ *lg[1+△/x] =lg[1+△/x]^(1/△) =lg[1+△/x]^(x/x△) ...
f'(x)=[f(x+△)-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x) =lg[(x+△)/x]/△ =1/△ *lg[1+△/x] =lg[1+△/x]^(1/△) =lg[1+△/x]^(x/x△) =lg[1+△/x]^[(x/△)*1/x] =1/x*lg[1+△/x]^[(x/△)...
-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x)=lg[(x+△)/x]/△ =1/△ *lg[1+△/x]=lg[1+△/x]^(1/△)=lg[1+△/x]^(x/x△)=lg[1+△/x]^[(x/△)*1/x]=1/x*lg[1+△/x]^[(x/△)当△->0时 [1+△/x]^[(x/△)->e ∴f'(x)=1/x *lge ...
f'(x)=[f(x+△)-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x) =lg[(x+△)/x]/△ =1/△ *lg[1+△/x] =lg[1+△/x]^(1/△) =lg[1+△/x]^(x/x△) =lg[1+△/x]^[(x/△)*1/x] =1/x*lg[1+△/x]^[(x/△)当...
-f(x)]/(x+△-x)=[lg(x+△)-lgx]/(x+△-x)=lg[(x+△)/x]/△ =1/△ *lg[1+△/x]=lg[1+△/x]^(1/△)=lg[1+△/x]^(x/x△)=lg[1+△/x]^[(x/△)*1/x]=1/x*lg[1+△/x]^[(x/△)当△->0时 [1+△/x]^[(x/△)->e ∴f'(x)=1/x *lge ...