例3求y=tanx的导数 解y=(anx)'= SIn d cos (sin x)'cos x-sin x(cos x) 2 cos 2 cos+sin x sec d cos (tan x)=sec x 同理可得(cotx) Csc。例3 求 y = tan x的导数 . 解 ) cos sin  = (tan ) = (  x x y x x x x x x 2 cos (sin ) cos − sin (cos ) = x x x 2 2 2 cos cos + sin = x x 2 2 sec cos 1 = = (tan ) sec . 2 即 x  = x (cot ) csc . 2 同理可得 x  = − x