How do you find dy/dx by implicit differentiation?

Question

e^(x/y)=3x-3y

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Answer 1 · 2016-11-04T19:19:41

#dy/dx=(ye^(x/y)-3y^2)/ (x e^(x/y)-3y^2)#

#e^(x/y)=3x-3y#

#1/y e^(x/y)-x/y^2 e^(x/y)dy/dx =3-3dy/dx#

#1/ye^(x/y)-3=x/y^2 e^(x/y)dy/dx-3dy/dx#

#(e^(x/y)-3y)/y=dy/dx (x/y^2 e^(x/y)-3)#

#(e^(x/y)-3y)/y=dy/dx ((x e^(x/y)-3y^2)/y^2)#

#dy/dx =(e^(x/y)-3y)/y *y^2/ (x e^(x/y)-3y^2)#

#dy/dx=(ye^(x/y)-3y^2)/ (x e^(x/y)-3y^2)#