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

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)]

一看就是武汉轻工大学的大一小学弟学妹