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Math Help - Implicit Differentiation Check

  1. #1
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    Implicit Differentiation Check

    find dy/dx using implicit differentiation

    cos(x)+tan(xy)+8=7

    First i change to cos(x)+tan(xy)+1=0

    Im using -Fx(x,y) / Fy(x,y)

    Fx= -sin(x)+ysec2(xy)

    Fy= xsec2(xy)

    dy/dx= sin(x)+ysec2(xy) / xsec2(xy)

    Right or wrong? Thanks.
    Last edited by tastylick; October 8th 2013 at 05:35 PM.
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  2. #2
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    Re: Implicit Differentiation Check

    If  F_x= -sin(x)+ysec^2(xy) wouldn't -F_x= sin(x)-ysec^2(xy) ?
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  3. #3
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    Re: Implicit Differentiation Check

    Yes. I believe so. Thats what i did on my last step. But i dont know where to go from there to get the final answer.
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  4. #4
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    Re: Implicit Differentiation Check

    Quote Originally Posted by tastylick View Post
    Yes. I believe so. Thats what i did on my last step. But i dont know where to go from there to get the final answer.
    I think what MadSoulz was getting at is that you wrote \dfrac{dy}{dx} = \dfrac{\sin(x) + y\sec^2(xy)}{x\sec^2(xy)}. The numerator is not -F_x which would have a negative sign between \sin(x) and y\sec^2(xy).
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  5. #5
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    Re: Implicit Differentiation Check

    So it should be

    dy/dx= sin(x)-ysec2(xy) / xsec2(xy) correct.

    But where to take it from there?
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  6. #6
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    Re: Implicit Differentiation Check

    Quote Originally Posted by tastylick View Post
    But where to take it from there?
    I believe you're done.
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  7. #7
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    Re: Implicit Differentiation Check

    Ah ok. I emailed my professor about this question and it turns out it was a mistake on her part. Yes my answer is correct. Thank you all for the help.
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