Question

求导化简问题

求导化简问题怎么化简成右边的最终答案

Answer 1

6)
(u/v)' = (u'v - uv')/v^2
y' = [(sinx)'(1+cosx) - sinx(1+cosx)' ] / (1+cosx)^2
= [cosx + cosx^2 + sinx^2] / (1+cosx)^2
= [cosx + 1] / (1+cosx)^2
= 1/(1+cosx)

8)
y = 2sinx + sinx/cosx
y' = 2cosx + [(sinx)'cosx - sinx(cosx)']/cosx^2
= 2cosx + [cosx^2 + sinx^2]/cosx^2
= 2cosx + secx^2