设函数y=x^x+ln(arctan5x),求其导数dy / dx、微分dy

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/06 00:21:16
设函数y=x^x+ln(arctan5x),求其导数dy / dx、微分dy
x){nϦnH,J.I3yi붧S*R*74>ݷiG[JMR>% l(RV!5N"'BSA[!'/]?"R?IU44Zц@+(6NCPSlaȺLڐuB-Mؔ <;P1

设函数y=x^x+ln(arctan5x),求其导数dy / dx、微分dy
设函数y=x^x+ln(arctan5x),求其导数dy / dx、微分dy

设函数y=x^x+ln(arctan5x),求其导数dy / dx、微分dy
y = e^(xlnx) + ln[arctan(5x)]
dy/dx = e^(xlnx)[lnx + 1] + 1/arctan(5x)*[1 + (5x)^2]^(-1)*5
= x^x[lnx + 1] + 5/{arctan(5x)[1 + (5x)^2]}
dy = [x^x[lnx + 1] + 5/{arctan(5x)[1 + (5x)^2]}]dx