dy/dx=t ÔõôÇód2y/dx2

d2y/dx2ÊéÉÏÊÇ˵d²y/dx²=d(dy/dx)/dx=dy'/dx¾ÍÊÇ˵d²y/dx²±íʾµÄÊǶÔy'ÔÙÇóÒ»´Îµ¼¶øÒѾ­...


d2y/dx2ÔõôËã - °Ù¶È¾­Ñé

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dx/dy =y,d2y dx2ÔõôÇó

Á½±ß¶ÔxÇóµ¼£¬µÃd^2y/dx^2=(-1/y^2)dy/dx (ÏȶÔyÇóµ¼£¬ÔÙ³ËÒÔy¶ÔxµÄµ¼Êý)=-1/(y^3)


d2y/dx2µÈÓÚʲô

d^2y/dx^2=d/dx(dy/dx)=d/dt(dy/dx)/(dx/dt)


d^2y/dx^2ÈçºÎ¼ÆËã?

d^2y/dx^2$ ±íʾº¯Êý $y$ ¶Ô $x$ µÄ¶þ½×µ¼Êý£¬¿ÉÒÔͨ¹ý¶Ô $dy/dx$ ÔÙ´ÎÇ󵼵õ½¡£¾ßÌåµØ£¬ÎÒÃÇ¿ÉÒÔʹÓÃÒÔϹ«Ê½¼ÆË㣺\...


...f(t),f''(t)´æÔÚÇÒ²»Îª0,Çód2y/dx2.ÕâÀïûÓи´ºÏÇóµ¼µÄ...

/dt * dt/dx = dt/dt * dt/dx =1/(dx/dt)=1/f "(t)ËùÒÔy¶ÔxµÄ¶þ½×µ¼Êýd²y/dx²=1/f "(t)...


ÈçºÎÇód^2y/ dx^2¹«Ê½

d^2y/dx^2 = [d(dy/dx)/dt]/(dx/dt)= ¡¾2(y+t)(dy/dt+1)e^[(y+t)^2](3t^2+2)-6t{e^[(y+t)^2]-1...


...dy2/dx2 µ½µ×ÊDZí´ïʲô Ôõô»¯µÄ

d2y/dx2±íʾ½«dy/dxÔٴζÔxÇóµ¼Êý£¬Ò²¾ÍÊǶþ½×µ¼£¬·½·¨Ò»¾ÍÊÇΪÁ˵õ½¶þ½×µ¼ºÍÒ»½×µ¼µÄ¹Øϵ£¬È»ºó...


Éèy=x2lnx,Çódy¼°d2y/dx2

Óõ¼Êý³Ë»ýµÄ¹«Ê½ dy=x(lnx)'+lnx


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