作业帮求In(secx+tanx)的导数?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/18 03:15:52
求In(secx+tanx)的导数?
ln(secx+tanx)
=ln(1/cosx+sinx/cosx)
=ln[(sinx+1)/cosx]
所以In(secx+tanx)的导数
=1/(sinx+1)/cosx * [(sinx+1)/cosx]'
=cosx/(sinx+1)*[cosx*cosx-(sinx+1)*(-sinx)]/cos^2x
=cosx/(sinx+1)*(cos^2x +sin^2x+sinx)/cos^2x
=cosx/(sinx+1)*(1+sinx)/cos^2x
=1/cosx
=ln(1/cosx+sinx/cosx)
=ln[(sinx+1)/cosx]
所以In(secx+tanx)的导数
=1/(sinx+1)/cosx * [(sinx+1)/cosx]'
=cosx/(sinx+1)*[cosx*cosx-(sinx+1)*(-sinx)]/cos^2x
=cosx/(sinx+1)*(cos^2x +sin^2x+sinx)/cos^2x
=cosx/(sinx+1)*(1+sinx)/cos^2x
=1/cosx