高数复合函数求导 y=ln cos e^x,求dy/dx
问题描述：
高数复合函数求导 y=ln cos e^x,求dy/dx
答
dy/dx
=y'=1/[cos(e^x)]×[cos(e^x)]'
=1/[cos(e^x)]×[cos(e^x)]'
=1/[cos(e^x)]×[-sin(e^x)]×(e^x)'
=1/[cos(e^x)]×[-sin(e^x)]×(e^x)
=-(e^x)[tan(e^x)]
答
dy/dx=(1/cos e^x)*(-sin e^x)*e^x=-e^x*tan e^x
答
dy/dx=[d(ln cos e^x) / d(cos e^x)] × [d(cos e^x) / e^x] × [d(e^x) / x]
=[1/(cos e^x)] × [- sin e^x] × [e^x]
= - (tan e^x) × e^x