Question

What is the implicit derivative of `4= (x+y)^2 -3xy`?

Answer 1

I found: `(dy)/(dx)=(-2x+y)/(2y-x)`

Explanation:

You need to derive `y` as well as it represents a function of `x`.
So, for example, if you have `y^2` the derivative will be `2y(dy)/(dx)`.
In your case:
`0=2(x+y)*(1+1(dy)/(dx))-3y-3x(dy)/(dx)`
`0=2x+2x(dy)/(dx)+2y+2y(dy)/(dx)-3y-3x(dy)/(dx)`
We collect `(dy)/(dx)`:
`(dy)/(dx)=(-2x+y)/(2y-x)`