简单求导10分

f(x)=sinΧ／3倍根号cosΧ
f(x)=sinx/[3(cosx)^1/2]
f'(x)=[(sinx)'*3(cosx)^1/2-sinx*(3(cosx)^1/2)']/[3(cosx)^1/2]^2
=[cosx*3(cosx)^1/2-sinx*(3*(1/2*(cosx)^(-1/2)*(-sinx))]/(9cosx)
=[3(cosx)^(3/2)+3/2*sinx*(cosx)^(-1/2)]/(9cosx)
=[(cosx)^(3/2)+1/2*tanx]/(3cosx)

lnf(x)=lnsinx-3/2lncosx
两边求导得f`(x)/f(x)=cosx/sinx+3sinx/2cosx
f`(x)=f(x)[cotx+3/2tanx]
=sinΧ／3倍根号cosΧ(cotx+3/2tanx)