cos^2(xy)ÔõôÇóµ¼

¶ÔyÇóµ¼:= -2cos(xy)*sin(xy)*x= -x*sin(2xy) ½âÎö¿´²»¶®?Ãâ·Ñ²é¿´Í¬ÀàÌâÊÓƵ½âÎö


(cosxy)^2µÄµ¼Êý

-sin2x¡£¸ù¾ÝÊýѧµÄÇóµ¼¹«Ê½À´¼ÆËã(cosx)^2µÄµ¼ÊýΪ£ºy=(cosx)^2y=2cosx*(cosx)=-2cosx*sinx='-sin2x¡£


cos(xy^2)=x+2yÇóµ¼ y=x^1/xÇóµ¼

cos(xy^2) = x+2y -sin(xy^2) .( y^2 + 2xy.y') = 1+ 2y'[2+ 2xysin(xy^2)]y' = -(1 + y^2sin(xy^2) )y' =-(1 + y^2sin(xy^2) ...


Ò»¸ö¸ßÊýÎÊÌâ?¼ÆËã¶þÖØ»ý·Ö¡Ò¡ÒXYCOS(XY^2)dXdY=Æä °®ÎÊ...

cos£¨XY^2£©dXdY= =¡Ò{0¡ú¦Ð/2}X[¡Ò{0¡ú2}Ycos(XY^2)dY]dX= =(1/2)¡Ò{0¡ú¦Ð/2}[¡Ò{0¡ú2}cos(XY^2)d(XY^2)]dX= ...


cos(xy)¿ÉÒÔÓÃcosx¡¢cosyµÈ±íʾÂð?

µ±È»¿ÉÒÔÁË cos£¨xy£©=cosxcosy-sinxsiny siny+cosy=1 Ò»ÁªÁ¢¾ÍÐÐÁË ÐÞ¸Ä Ã»×¢Ò⣬ÎҵĹø()¶ªÁ³¡£²»...


cosƽ·½(xy)ºÍsinƽ·½(xy)ÔõÑùÇóµ¼

2cos(xy)(-sin(xy))(x+y) 2sin(xy)cos(xy)(x+y)


cos(xy)=(xy)^2ÇódyÇë¸ßÈ˽âÎöÒ»ÏÂ

Á½Ãæ¶ÔxͬʱÇóµ¼µÃ-sin(xy)(y+xy')=2xy(y+xy')ÕûÀíµÃ -ysin(xy)-2xy²=[xsin(xy)+2x²y]y'y'=-[ysin(xy)+2xy²]/[xsin(xy)+2x&sup2...


Çó΢·Ö·½³Ìy'+y=xcos2xµÄÒ»¸öÌؽâ Óø¨Öú·½³ÌÔõô×ö - °Ù¶ÈÖª ...

Çó΢·Ö·½³ÌxY+Y'=1µÄ½â Åä·½·¨,Á½±ß³ËÒÔ e^(x^2/2)£º xy + y' £½ 1 x e^(x^2/2) y + e^(x^2/2) y' £½ e^(x^2/2) [ e^(x^2/2...


ÇóÓÉ·½³Ìcos(xy)=x^2*y^2 ËùÈ·¶¨µÄyµÄ΢·Ö

-sin(xy)[ydx+xdy]=2xy^2*dx+x^2*2ydy-sin(xy)ydx-sin(xy)xdy=2xy^2*dx+2x^2*ydy-2x^2*ydy-sin(xy)xdy=2xy^2*dx+sin(xy)ydx-[2x^2*y+sin(xy)x...


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