（sin（x-1）／cos（x-1））^2.求导!
问题描述：
（sin（x-1）／cos（x-1））^2.求导!
答
[sin(x-1)/cos(x-1)]^2
{[sin(x-1)/cos(x-1)]^2}'
=2[sin(x-1)/cos(x-1)]{[cos(x-1)]^2+[sin(x-1)]^2}/{[cos(x-1)]^2}
=2sin(x-1)/{[cos(x-1)]^3}
=2tan(x-1)/{[cos(x-1)]^2}
=2tan(x-1)[sec(x-1)]^2
答
[sin(x-1)/cos(x-1)]²=tan²(x-1)
所以原式=2tan(x-1)×sec²(x-1)×1
=2tan(x-1)sec²(x-1)