设y=ln(tanx+secx),求dy/dx

问题描述:

设y=ln(tanx+secx),求dy/dx

y=ln(tanx+secx),
y'=1/(tanx+secx)*(tanx+secx)'
=(sec^2x+secxtanx)/(tanx+secx)
=secx(cosx/cosx+sinx/cosx)/(sinx/cosx+1/cosx)
=(1+tanx)/(1+sinx)