设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则 dy/dx 感激不尽

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设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则dy/dx感激不尽设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则dy/dx感激不尽设函数y=y(x)由方程x^(y)+ylnx

设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则 dy/dx 感激不尽
设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则 dy/dx 感激不尽

设函数y=y(x)由方程x^(y)+ylnx+4=0确定,则 dy/dx 感激不尽
x^(y)+ylnx+4=0
两边同时对x进行求导,得:[e^(ylnx)]'+(ylnx)'=0
e^(ylnx)*(ylnx)'+(ylnx')=0
(x^y+1)*(ylnx)'=0
所以(ylnx)'=0,即y'lnx+y/x=0,所以y'=-y/(xlnx)
即dy/dx=-y/(xlnx)