Implicit differentiation help (Getting right answer, wrong signs)

[rsjrv99]

This should be simple. I keep getting the right answer but the wrong signs for almost every problem I do. I have evaluated every problem extensively and can't figure out how they are getting different signs for their answers in comparison to mine.

Here is an example problem, I hope it is clear enough. The added in paint brush is just to show you the cancelling out there that I forgot to add. I used the product rule and the chain rule here

 

[Ishuda]

This should be simple. I keep getting the right answer but the wrong signs for almost every problem I do. I have evaluated every problem extensively and can't figure out how they are getting different signs for their answers in comparison to mine.

Here is an example problem, I hope it is clear enough. The added in paint brush is just to show you the cancelling out there that I forgot to add. I used the product rule and the chain rule here

View attachment 4652

Those are the same answers.
$\displaystyle \dfrac{x\space (1 - y^2)}{y\space (x^2 - 1)}\space =\space \dfrac{x\space (1 - y^2)}{y\space (x^2 - 1)} \dfrac{(-1)}{(-1)}\space =\space \dfrac{x\space (1 - y^2)\space (-1)}{y\space (x^2 - 1)\space (-1)}\space =\space \dfrac{x\space ( y^2 - 1)}{y\space (1 - x^2)}$

 

[rsjrv99]

Those are the same answers.

So this derivative can have both a positive and negative value referring to two parts of the function at a given x value?

Like a circle, upper semicircle value is positive, while bottom semicircle is negative...


I saw your edit just now, that makes sense and what I was attempting, but for whatever reason I was thinking -1/-1 was -1 which would change sign on the other half of the equation...

OH THE SIMPLE MISTAKES OF MATH!

Thank you!