# Math Help - Implicit Differentiation - Check my work?

1. ## Implicit Differentiation - Check my work?

Hello, I'm doing an AP Cal AB practice test, and I'm having trouble with one of the problems. I think that I'm solving the problem correctly, but I must be doing something wrong since my answer is not one of the choices. Seeing how this was on a previous AP exam, I don't think it's likely that the choices were written incorrectly. Will you check over my work?

2. Originally Posted by pocketasian
Hello, I'm doing an AP Cal AB practice test, and I'm having trouble with one of the problems. I think that I'm solving the problem correctly, but I must be doing something wrong since my answer is not one of the choices. Seeing how this was on a previous AP exam, I don't think it's likely that the choices were written incorrectly. Will you check over my work?
I believe your answer is tha same as (a) - factor the negative 1!

3. Originally Posted by pocketasian
Hello, I'm doing an AP Cal AB practice test, and I'm having trouble with one of the problems. I think that I'm solving the problem correctly, but I must be doing something wrong since my answer is not one of the choices. Seeing how this was on a previous AP exam, I don't think it's likely that the choices were written incorrectly. Will you check over my work?
It looks like your answer is equivalent to A. If you factor out -1 in your numerator you should get the same syntax as answer A (both are correct still)

4. So even though there aren't parentheses around 2x+y in choice A, it can still be considered as having a -1 factored out? I would think -(2x+y) would make more sense...

5. Originally Posted by pocketasian
So even though there aren't parentheses around 2x+y in choice A, it can still be considered as having a -1 factored out? I would think -(2x+y) would make more sense...
Option A is unclear. Do you mean $- \frac{2x+y}{x+3y^2}$ or

$\frac{-2x+y}{x+3y^2}$

6. Originally Posted by e^(i*pi)
Option A is unclear. Do you mean $- \frac{2x+y}{x+3y^2}$ or

$\frac{-2x+y}{x+3y^2}$
It's written as
$- \frac{2x+y}{x+3y^2}$
I guess there's a difference then?

7. Originally Posted by pocketasian
It's written as
$- \frac{2x+y}{x+3y^2}$
I guess there's a difference then?
Yes, there is.

$-\frac{2x+y}{x+3y^2} = (-1)\frac{2x+y}{x+3y^2} = \frac{(-1)(2x+y)}{x+ey^2} = \frac{-2x-y}{x+3y^2} \neq \frac{-2x+y}{x+3y^2}$