(cotx)`=(cosx/sinx)`
=[(cosx)`sinx-cosx(sinx)`]/sin²x(商的求导公式)
=[-sinxsinx-cosxcosx]/sin²x
=[-sin²x-cos²x]/sin²x
=-1/sin²x
(-1/sinx)′ = 1/sinx×(sinx)′ = cosx/sinx = cotx × cscx
所以cotx的二阶导数是cotx×cscx
原创 | 2022-10-11 00:09:54 |浏览:1.6万
(cotx)`=(cosx/sinx)`
=[(cosx)`sinx-cosx(sinx)`]/sin²x(商的求导公式)
=[-sinxsinx-cosxcosx]/sin²x
=[-sin²x-cos²x]/sin²x
=-1/sin²x
(-1/sinx)′ = 1/sinx×(sinx)′ = cosx/sinx = cotx × cscx
所以cotx的二阶导数是cotx×cscx