f(x)=(x+xlnx)/(x-1)的导数?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/08 07:27:43
f(x)=(x+xlnx)/(x-1)的导数?f(x)=(x+xlnx)/(x-1)的导数?f(x)=(x+xlnx)/(x-1)的导数?详解在图片里,放大就好看了用导数的除法法则[(1+lnx+1)

f(x)=(x+xlnx)/(x-1)的导数?
f(x)=(x+xlnx)/(x-1)的导数?

f(x)=(x+xlnx)/(x-1)的导数?
详解在图片里,放大就好看了

用导数的除法法则
[(1+lnx+1)(x-1)-(x+xlnx)]/(x-1)^2=(x-2-lnx)/(x-1)^2

具体过程:
f'(x)={(x+xlnx)'(x-1)-(x+xlnx)(x-1)'}/(x-1)^2
={(1+x.1/x+lnx)(x-1)-(x+xlnx)}/(x-1)^2
=(x-2-lnx)/(x-1)^2