西安毛子科技大学函数的求导法则XIDIAN UNIVERSITY例2 求证(tanx)= sec2 x，(cscx)'=-cscxcotx,(sin x)'cos x -sin x(cosx)sin x证(tan x)':COSxcos? xcos? x +sin? x= Sec2 xcos?x-(sin x)-coS xcscxsin xsin? xsin? x=-cscxcot x类似可证：(cot x)'=-csc2 x，(secx)'= secxtan x,函数的求导法则 (csc ) x  = 1 sin x        2 sin x = −(sin ) x  2 sin x = 例2 求证 证 sin (tan ) cos x x x     =     = 2 cos x (sin ) cos x x  −sin (cos ) x x  = 2 cos x 2 cos x 2 +sin x 2 = sec x−cos x = −csc cot x x 类似可证: 2 (cot ) csc , x x  = − (sec ) sec tan . x x x  =