Question

求下列函数的导数 1、y=(1-lnx)/(1+lnx) 2、y=(xtanx)/(1+x^2) 3、y=x^1/3 (1-cosx)

Answer 1

1、
y‘= [(1-lnx)’(1+lnx) - (1-lnx)(1+lnx)'] /(1+lnx)^2
=[-1/x(1+lnx) - (1-lnx)1/x) ] / (1+lnx)^2
=[-1/x [(1+lnx)+(1-lnx)] / (1+lnx)^2
= （-2/x)/(1+lnx)^2
= -2[/x(1+lnx)^2]
2、
tanx的导数是1/(cosx)^2
y'=[(xtanx)’(1+x^2) - (xtanx)(1+x^2)'] / (1+x^2)^2
=[ (tanx+ x/(cosx)^2) (1+x^2) - (xtanx)2x ] / (1+x^2)^2
3、
y'=(x^1/3)' (1-cosx) + (x^1/3) (1-cosx)'
=1/3* x^(-2/3) *(1-cosx) + (x^1/3)sinx
=[x^(-2/3) (1-cosx) ]/3 + (x^1/3)sinx