How do you implicitly differentiate # x/y = - x^2 + y^2 -4#?

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Answer 1 · 2016-11-04T20:23:46

#dy/dx=(y+2xy^2)/(2y^3+x)#

#x/y=-x^2+y^2-4#

#1/y-x/y^2 dy/dx=-2x+2y dy/dx#

#1/y+2x=2y dy/dx+x/y^2 dy/dx#

#(1+2xy)/y=(2y+x/y^2)dy/dx#

#(1+2xy)/y=((2y^3+x)/y^2)dy/dx#

#dy/dx=(1+2xy)/y *y^2/(2y^3+x)#

#dy/dx=(y+2xy^2)/(2y^3+x)#