Question

find 2xy+y^2=x+y using implicit differentiation

Answer 1

I wish I was able to explain this well, but it's just difficult, to put into words lol.
I assume you have to take the derivative with respect to x.
So, there are a mix of x and y terms in this equation. There is x, which you can take the derivative directly. And there is y, which is a function of x, so you have to take the derivative 'implicitly'.

Answer 2

Let's say I have y = xy.
If I wanna derive it implicitly, the left side becomes y'.
And on the right side, I'd have to use the product rule. I assume you know how to do that.
\[\frac{d}{dx}[xy] = x*y' + y*1\]
You still use product rule, but when you see a 'y' term, you'll have to put it in prime terms, or implicit derivatives.

Answer 3

I see what your saying, it is much better explained what the d/dx mean than the do in class

Answer 4

Just depends on the teacher or resource I guess lol. I've heard more bad stories about calculus teachers lol.