求导:y = ( tan x )^3 [为什么等于3 ( sec x )^4 - 3 ( sec x )^2 ]

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求导:y = ( tan x )^3 [为什么等于3 ( sec x )^4 - 3 ( sec x )^2 ]

求导:y = ( tan x )^3 [为什么等于3 ( sec x )^4 - 3 ( sec x )^2 ]
求导:y = ( tan x )^3 [为什么等于3 ( sec x )^4 - 3 ( sec x )^2 ]

求导:y = ( tan x )^3 [为什么等于3 ( sec x )^4 - 3 ( sec x )^2 ]
y=( tan x )^3
y'=3( tan x )^2*(tanx)'
=3( tan x )^2*sec^2x
=3sin^2x*sec^2x*sec^2x
=3seC^4x*sin^2x
=3seC^4x*(1-cos^2x)
=3sec^4 x -3sec^4xcos^2x
=3sec^4 x -3sec^2 x

y'=3tan²x*(tax)'
=3tan²x*sec²x
=3(sec²x-1)sec²x
=3sec⁴x-3sec²x