sinx^2导数等于多少 为什么(sinx)^2导数等于2sinx*cosx
\u4ec0\u4e48\u7684\u5bfc\u6570\u7b49\u4e8e(sinx)^2\u8fd9\u662f\u4e00\u4e2a\u590d\u5408\u51fd\u6570
\u4ee4sinx=u
\u5219\u95ee\u9898\u53d8\u4e3a \u4ec0\u4e48\u7684\u5012\u6570\u662fu^2
\u52191/3u^3\u5f97\u5bfc\u6570\u662fu^2
\u53c8\u56e0\u4e3au=sinx
\u5219-(cosx)'=sinx
\u6240\u4ee5\u6700\u7ec8 -1/3(sinx\uff09^3*cosx\u5f97\u5bfc\u6570\u5c31\u662f(sinx)^2
u = sin x²
u'= 2x cos x²
\u8fd9\u662f\u590d\u5408\u51fd\u6570\u6c42\u5bfc\uff1a\u4ee4 y = x² u = sin y du/dx \uff1d(du/dy)*(dy/dx) \uff1d cos y * 2x \uff1d2x cos x²
先求sinu的导数，再求u=x^2的导数
=cosx^2*2x
绛旓細sinx^2鐨勫鏁颁负锛歴in2x 鎺ㄥ杩囩▼锛氬厛姹傚鍑芥暟y=(sinx)^2,鍗2sinx,鍐嶆眰鍐呭嚱鏁皊inx鐨勫,鍗砪osx.鏁(sinx)^2鐨勫鏁颁负2sinxcosx,涔熷氨鏄痵in2x 瀵兼暟鐨勬剰涔夛細濡傛灉鍑芥暟y=f锛坸锛夊湪寮鍖洪棿鍐呮瘡涓鐐归兘鍙锛屽氨绉板嚱鏁癴锛坸锛夊湪鍖洪棿鍐呭彲瀵笺傝繖鏃跺嚱鏁皔=f锛坸锛夊浜庡尯闂村唴鐨勬瘡涓涓‘瀹氱殑x鍊硷紝閮藉搴旂潃涓...
绛旓細sinx^2鐨勫鏁版槸sin2x銆傝繖鏄竴涓鍚堝嚱鏁扮殑姹傚闂锛屽厛姹傚鍑芥暟y=(sinx)^2锛屽嵆2sinx锛屽啀姹傚唴鍑芥暟sinx鐨勫锛屽嵆cosx.鏁(sinx)^2鐨勫鏁颁负2sinxcos锛屼篃灏辨槸sin2x銆傝В棰樿繃绋 [(sinx)^2]'=2(sinx)(sinx)'=2sinxcosx=sin2x 鎵浠ワ細(sinx)^2鐨勫鏁颁负sin2x (sin2x)'=2cos2x 鎵浠ワ細(sinx)^2...
绛旓細鏂规硶濡備笅鍥炬墍绀猴紝璇蜂綔鍙傝冿紝绁濆涔犳剦蹇細
绛旓細sinx骞虫柟鐨瀵兼暟=2sinxcosx=sin2x
绛旓細鍥炵瓟锛2(cosx^2-sinx^2)
绛旓細绛旓細[(sinx)^2]'=2(sinx)(sinx)'=2sinxcosx=sin2x 鎵浠ワ細(sinx)^2鐨勫鏁颁负sin2x (sin2x)'=2cos2x 鎵浠ワ細(sinx)^2鐨勫鏁扮殑瀵兼暟鏄2cos2x
绛旓細澶嶅悎鍑芥暟姹傚锛屽厛姹俿inu鐨瀵兼暟锛屽啀姹倁=x^2鐨勫鏁 =cosx^2*2x
绛旓細褰揻(x)=a(x)*b(x)f'(x)=a'(x)b(x)+a(x)b'(x)閭ｄ箞 f(x)=sinx骞虫柟=sinx*sinx 鍒檉'(x)=cosxsinx+sinxcosx=2sinxcosx=sin2x
绛旓細璁緁(x)鍦▁=t澶勭殑瀵兼暟涓f'(t)f'(t)=lim [sin(x^2)-sin(t^2)]/(x-t) 鍏朵腑x->t =lim 2cos[(x^2+t^2)/2]路sin[(x^2-t^2)/2]/(x-t) 鍜屽樊鍖栫Н鍏紡 =lim 2cos[(t^2+t^2)/2]*((x^2-t^2)/2) / (x-t) sin((x^2-t^2)/2)~((x^2-t^2)...
绛旓細鈭(sin²x)锛囷紳2sinxcosx锛漵in2x 甯哥敤瀵兼暟鍏紡锛1銆亂=c(c涓哄父鏁) y'=0 2銆亂=x^n y'=nx^(n-1)3銆亂=a^x y'=a^xlna锛寉=e^x y'=e^x 4銆亂=logax y'=logae/x锛寉=lnx y'=1/x 5銆亂=sinx y'=cosx 6銆亂=cosx y'=-sinx 7銆亂=tanx y'=1/cos^2x 8銆亂=cotx ...
