Question

How do you differentiate `e^(xy)+x^2-y^2=0`?

Answer 1

You have an Implicit Function in which `y` is function of `x` so you have to derive it as well.
You get:
`e^(xy)*(1*y+xdy/dx)+2x-2ydy/dx=0`
where you used the Product Rule for the exponent of `e`;

`ye^(xy)+xe^(xy)dy/dx+2x-2ydy/dx=0`

`dy/dx[xe^(xy)-2y]=-2x-ye^(xy)`

finally:

`dy/dx=-(2x+2ye^(xy))/(xe^(xy)-2y)`

Hope it helps