函数f（x）=sin^2x求导 f（x）＝sin2x怎么求导？
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f(x) = sin2x = sinu, \u5176\u4e2d u = 2x
f'(x) = cosu\u00b7(u)' = cos2x (2x)' = 2cos2x
∴f'(x)=sin2x
f'（x）=2sinx*cosx=sin(2x)
绛旓細f(x)=(sinx)^2 浠(x)=sinx f(g(x))=g(x)^2 f'(g(x))=2*g(x)g'(x)=cosx [f(g(x))]'=f'(g(x))*g'(x)=2*g(x)*g'(x)=2*sinx*cosx=sin2x 鏈涢噰绾冲皬濂冲瓙绛旀涓烘弧鎰忕瓟妗 璋㈣阿
绛旓細[cos(e^x) ]'= 2 cos(e^x) *[-sin(e^x)] * (e^x)'= 2 cos(e^x) *[-sin(e^x)] * e^x = - sin(2e^x) * e^x [e^(sin^2x)]' = ( sin^2x)' * e^(sin^2x)鍒╃敤绗1涓殑缁撴灉 = sin(2x) * e^(sin^2x)姹傚鐨勯『搴忔槸鏈夊鍚鍑芥暟鐨勫灞傚埌鍐呭眰 ...
绛旓細杩愮畻鏂规硶鏈変互涓嬩袱绉嶏細1.(sin²x)' = 2sinx(sinx)' = 2sinxcosx = sin2x銆2.(sin²x)' = [(1-cos2x)/2]' = [1/2 - (cos2x)/2]' = 0 - ½(-sin2x)(2x)' = ½(sin2x)脳2 = sin2x銆
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绛旓細鍏蜂綋鍥炵瓟濡備笅锛歽=sin^2xcos^2x =(sinxcosx)^2 =1/4(4sinxcosx)^2 = 1/4(sin2x)^2 y'=1/4x2sin2xcos2x(2)=sin2xcos2x =1/2sin4x y=1/4(u)^2 u=sinv v=2x 瀵兼暟鐨勮绠楋細璁＄畻宸茬煡鍑芥暟鐨勫鍑芥暟鍙互鎸夌収瀵兼暟鐨勫畾涔夎繍鐢ㄥ彉鍖栨瘮鍊肩殑鏋侀檺鏉ヨ绠楋紝鍦ㄥ疄闄呰绠椾腑锛屽ぇ閮ㄥ垎甯歌鐨勮В鏋愬嚱鏁伴兘...
绛旓細sin^2(x)'=2sin(x)*(sin(x))'=2sinxcosx=sin2x
绛旓細楹﹀厠鍔虫灄灞曞紑寮忥細鑻鍑芥暟f(x)鍦ㄥ紑鍖洪棿锛坅锛宐锛夋湁鐩村埌n+1闃鐨勫鏁锛屽垯褰撳嚱鏁板湪姝ゅ尯闂村唴鏃讹紝鍙互灞曞紑涓轰竴涓叧浜巟澶氶」寮忓拰涓涓綑椤圭殑鍜岋細f(x)=f(0)+f(0)x+f(0)/2!•x^2,+f(0)/3!•x^3+鈥︹+f(n)(0)/n!•x^n+Rn 鍏朵腑Rn=f(n+1)(胃x)/(n+1)!•...
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绛旓細鍒濈瓑鍑芥暟鐨勫鏁鍙互浣跨敤瀵兼暟鐨勫熀鏈叕寮忓拰娉曞垯鏉ユ眰瑙ｃ備緥濡傦紝瀵逛簬鍑芥暟f(x) = x^2锛屾垜浠彲浠ヤ娇鐢ㄤ互涓嬪叕寮忔潵姹傚锛歠(x) = 2x锛屽浜庡鍚堝嚱鏁帮紝鎴戜滑鍙互浣跨敤閾惧紡娉曞垯鏉ユ眰瀵笺備緥濡傦紝瀵逛簬鍑芥暟f(x) = sin(2x)锛屾垜浠彲浠ヤ娇鐢ㄤ互涓嬪叕寮忔潵姹傚锛歠(x) = cos(2x) 脳 2鍙﹀锛屽浜庝竴浜涚壒娈婄殑鍒濈瓑鍑芥暟锛屽鎸囨暟...
