Question

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

Answer 1

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

Explanation:

`d/dx(y)=d/dx((x-y)^2-e^(xy)))`
`y'=2(x-y)*d/dx(x-y)-e^(xy)*d/dx(xy)`
`y'=2(x-y).(1-y')-(x.y'+y).e^(xy)`

solve the equation for y'
`y'=-(e^(xy)*y+2y-2x)/(x*e^(xy)-2y+2x+1`