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Math Help - Implicit Differentiation - Check my work?

  1. #1
    Newbie pocketasian's Avatar
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    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?
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  2. #2
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    Quote Originally Posted by pocketasian View Post
    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!
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  3. #3
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    Quote Originally Posted by pocketasian View Post
    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)
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  4. #4
    Newbie pocketasian's Avatar
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    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...
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  5. #5
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    Quote Originally Posted by pocketasian View Post
    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}
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  6. #6
    Newbie pocketasian's Avatar
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    Quote Originally Posted by e^(i*pi) View Post
    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?
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  7. #7
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    Quote Originally Posted by pocketasian View Post
    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}
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