高数复合函数求导 y=ln cos e^x,求dy/dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/08 00:13:10
高数复合函数求导y=lncose^x,求dy/dx高数复合函数求导y=lncose^x,求dy/dx高数复合函数求导y=lncose^x,求dy/dxdy/dx=[d(lncose^x)/d(cose

高数复合函数求导 y=ln cos e^x,求dy/dx
高数复合函数求导 y=ln cos e^x,求dy/dx

高数复合函数求导 y=ln cos e^x,求dy/dx
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

dy/dx=(1/cos e^x)*(-sin e^x)*e^x=-e^x*tan e^x

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)]