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求由方程ysinx-cos(xy)=0所确定的隐函数y=y(x)的导数dy\/dx
ysinx=cos(xy)两边分别求导 y'sinx+ycosx=-sin(xy)(y+xy')y'=-y(sin(xy)+cosx)\/(sinx+xsin(xy))
求下列由方程所确定的隐函数y=y(x)的导数dy\/dx
答：e^x-e^y-sin(xy)=0 两边对x求导：e^x -(e^y)y'-cos(xy)*(y+xy')=0 所以：[xcos(xy)+e^y]*y'=e^x-ycos(xy)所以：dy\/dx=y'= [e^x-ycos(xy) ] \/ [ xcos(xy)+e^y ]
隐函数的导数
回答：将方程右边化为0,那么 sinxy-y=0 令F(x,y)=sinxy-y dy\/dx=-Fx\/Fy=-(ycosxy)\/(xcosxy-1) 注意:求Fx,Fy时,分别将y,x看出一个常量来求
如何求三角函数的导数公式?
用隐函数求导法设F(x,y)=x-cos(xy)，则F'x=1+ysin(xy),F'y=xsin(xy)，所以dy\/dx=-F'x\/F'y=-[(1+ysin(xy)]\/[xsin(xy)]。三角函数求导公式：(sinx)'=cosx、(cosx)'=-sinx、(tanx)'=sec²x=1+tan²x。三角函数公式看似很多、很复杂，但只要掌握了三角函数的本质及...
求方程所确定的隐函数的导数dy\/dx:e的xy次方+ylnx=cos2x
由e^xy(y+xdy\/dx)+dy\/dx lnx+y\/x=-2sinx得 dy\/dx=(-ye^xy-y\/x-2sinx)\/(lnx+xe^xy)
求方程sin(xy)=x确定的隐函数的一阶导数。
方程两边对变量x求导有 d[sin(xy)]\/dx=dx\/dx cos(xy)*d(xy)\/dx=1 cos(xy)*(dx*y+x*dy)\/dx=1 cos(xy)*[y+x*(dy\/dx)]=1 所以：dy\/dx=[1-ycos(xy)]\/[xcos(xy)]
cos(xy)求导
当使用隐函数法求解F(x,y)=x-cos(xy)的导数时，我们需要对F关于x和y分别求导。F'x等于1加上y乘以sin(xy)，即F'x=1+ysin(xy)，而F'y则是x乘以sin(xy)，即F'y=xsin(xy)。因此，通过链式法则，dy\/dx的值为dy\/dx=-F'x\/F'y，即[-(1+ysin(xy))]\/[xsin(xy)]。三角函数求导并非...
求由方程cosx+eysinxy=1所确定的隐函数的导数y’(x)
求由方程cosx+eysinxy=1所确定的隐函数的导数y’(x)解：方程F(x，y)=cosx+eysin(xy)-1=0确定一个隐函数y=f(x)，求dy\/dx.dy\/dx=-[∂F\/∂x]\/[∂F\/∂y]=-[-sinx+ey²cos(xy)]\/[esin(xy)+exycos(xy)]=[sinx-ey²cos(xy)]\/[esin(xy...
求y=sinxy的隐函数的导数
解析：y=sin(xy)y'=cos(xy)●(xy)'y'=cos(xy)●(y+xy')y'[1-xcos(xy)]=ycos(xy)y'=ycos(xy)\/[1-xcos(xy)]
求sinxy=x+y的隐函数y的导数。谢谢!
回答：y`=1\/COSXY-1
