cos^2t的导数
负2sin2t。对于余弦函数求导，余弦函数的导数是正弦函数，由复合函数求导法则可知复合函数的导数等于各个函数的导数相乘，cos^2t这个复合函数可以看成两个函数分别是余弦函数和2t，cos^2t的导数应该是正弦函数乘以2，可得出cos^2t的导数是负2sin2t。绛旓細璐2sin2t銆傚浜庝綑寮﹀嚱鏁版眰瀵硷紝浣欏鸡鍑芥暟鐨勫鏁版槸姝ｅ鸡鍑芥暟锛岀敱澶嶅悎鍑芥暟姹傚娉曞垯鍙煡澶嶅悎鍑芥暟鐨勫鏁扮瓑浜庡悇涓嚱鏁扮殑瀵兼暟鐩镐箻锛宑os^2t杩欎釜澶嶅悎鍑芥暟鍙互鐪嬫垚涓や釜鍑芥暟鍒嗗埆鏄綑寮﹀嚱鏁板拰2t锛cos^2t鐨勫鏁搴旇鏄寮﹀嚱鏁颁箻浠2锛屽彲寰楀嚭cos^2t鐨勫鏁版槸璐2sin2t銆
绛旓細鎵浠ワ紝2(cost)^2=cos2t+1 鎵浠ワ紝(cost)^2=(1/2)(cos2t+1)鎵浠ワ紝(1/2)鈭(cos2t+1)dt=鈭(cost)^2dt
绛旓細绛旀鏄痶/2-(sin2t)/4+C 鍏蜂綋姝ラ濡備笅锛氣埆sin²tdt =鈭(1-cos2t)/2 dt =鈭1/2dt-鈭紙cos2t锛/2 dt =鈭1/2dt-1/4 d(sin2t)=t/2-(sin2t)/4+C (C涓轰换鎰忓父鏁帮級
绛旓細dx/dt=-2sintcost dy/dt=2sintcos2t dy/dx=-2sintcost/2sintcost=-1
绛旓細lny=xlncosx,涓よ竟姹瀵兼暟寰楋細y'/y=lncosx-x(sinx/cosx)=lncosx-xtanx 鎵浠ワ細y'=y(lncosx-xtanx)=(cos x)^x (lncosx-xtanx)
绛旓細鍏堟眰涓闃瀵兼暟锛歞x/dt = cost dy/dt = -2sin2t dy/dx = dy/dt 梅 dx/dt = -2sin2t/cost = -4sint cost / cost = -4sint ;鍐嶆眰浜岄樁瀵兼暟锛(dy/dx)/dt = -4cost dx/dt = cost (d^2y)/(dx^2) = (dy/dx)/dt 梅 dx/dt = -4cost / cost =-4 ...
绛旓細鍥剧墖宸茬粡鍋氬ソ锛屽凡缁忎紶杩涙潵浜嗭紝鍑犲垎閽熶箣鍚庯紝妤间富灏卞彲浠ョ湅鍒般
绛旓細x't=cost y't=-2sin2t dy/dx=y't/x't=-2sin2t/cost=-4sintcost/cost=-4sint
绛旓細浠=sint 鍒欏師寮=鈭(-蟺/2鈫捪/2)cost*costdt =鈭(-蟺/2鈫捪/2)(cos(2t)+1)/2dt =1/4鈭(-蟺/2鈫捪/2)cos(2t)d(2t)+鈭(-蟺/2鈫捪/2)dt/2 =sin(2t)/4|(-蟺/2鈫捪/2)+t/2|(-蟺/2鈫捪/2)=蟺/2
绛旓細x't=cost y't=-2sin2t dy/dx=y't/x't=-2sin2t/cost=-4sintcost/cost=-4sint
