(sin x)'cos x -sin x(cos x) cos cosx+sin x sec d cos cos 即(tanx)=sec2x 同理可得(cotx)=-csc2x 例4y=secx求y 解 (cos x sinx 1 Secy·tanx cos x cos cosx cosx 同理可得 (cscx)=-cscxcotxx 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 同理可得 (cot ) csc . 2 x  = − x 例4 y = sec x 求y 解         = x y cos 1 x x 2 cos (cos ) = − x x x x x sec tan cos 1 cos sin =  =  同理可得 (cscx) = −csc x  cot x