谁能交我做下这题y=5sec^7x-7sec^5x和y=lncosarctan（shx）求函数的导数过程最好写下

Question

谁能交我做下这题 y=5sec^7x-7sec^5x和y=lncosarctan（shx） 求函数的导数
过程最好写下

Answer 1

y'=(5sec^7x-7sec^5x)'
=5*7*(sec^6x)*(secx)'+7*5*(sec^4x)*(secx)'
=35*(sec^6x)* secx * tanx+35*(sec^4x)* secx * tanx
=35(sec^5x)tanx*(sec^2x - 1)
=35sec^5x * tan^3x
y'={ln[cos(arctanshx)]}'
=[cos(arctanshx)]'/[cos(arctanshx)]
又因为[cos(arctanshx)]'
=[-xin(arctanshx)]*(arctanshx)'
=[-xin(arctanshx)]*[1/(1+sh^2x)]*(shx)'
=[-xin(arctanshx)]*[1/(1+sh^2x)]*(chx)
=[-xin(arctanshx)]*[1/ch^2x]*(chx)
=[-xin(arctanshx)]*[1/chx]
所以y'=[cos(arctanshx)]'/[cos(arctanshx)]
={[-xin(arctanshx)]*[1/chx]} / [cos(arctanshx)]