作业帮高数题,y=y(x)由y²=f(xy)+sin(x+y)确定,f可微,求dy/dx
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高数题,y=y(x)由y²=f(xy)+sin(x+y)确定,f可微,求dy/dx
高数题,y=y(x)由y²=f(xy)+sin(x+y)确定,f可微,求dy/dx
高数题,y=y(x)由y²=f(xy)+sin(x+y)确定,f可微,求dy/dx
y²=f(xy)+sin(x+y)两边求导，
2yy'=f'(xy)(y+xy')+cos(x+y)(1+y')
整理
[2y-xf'(xy)-cos(x+y)]y'=yf'(xy)+cos(x+y)
因此
y'=[yf'(xy)+cos(x+y)]/[2y-xf'(xy)-cos(x+y)]
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