Question

How do you implicitly differentiate `y= (x-y) e^(xy)-xy^2`?

Answer 1

`y'=(e^(xy)+y(x-y)e^(xy)-y^2)/(1+e^(xy)-x(x-y)e^(xy)+2xy)`

Explanation:

Differentiating with respect to `x`

`y'=(1-y')e^(xy)+(x-y)e^(xy)(y+xy')-y^2-2xyy'`
so we get
`y'(1+e^(xy)-x(x-y)e^(xy)+2xy)=e^(xy)+y(x-y)e^(xy)-y^2`