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Math Help - Backwards derivative problem

  1. #1
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    Backwards derivative problem

    Before, I posted a problem about partial derivatives. Well, this time I have to use the partial derivative to find F(x,y), and I'm not really sure how to go about it. I am given the two following partial derivatives.

    (1) The derivative of F with respect to x is x^2 divided by y

    and

    (2) The derivative of F with respect to x is xe^xy
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by clockingly View Post
    Before, I posted a problem about partial derivatives. Well, this time I have to use the partial derivative to find F(x,y), and I'm not really sure how to go about it. I am given the two following partial derivatives.

    (1) The derivative of F with respect to x is x^2 divided by y

    and

    (2) The derivative of F with respect to x is xe^xy
    the same principle holds. integrate both with respect to x by treating y as a constant
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  3. #3
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    Quote Originally Posted by clockingly View Post

    (1) The derivative of F with respect to x is x^2 divided by y
    Let f(x)=y.

    That means,
    y'=x^2/y

    Thus,
    y'*y=x^2

    Thus,

    INT y*y' dx = INT x^2 dx +C (Substitution rule is used implicity).

    (1/2)y^2 = (1/3)x^3 +C
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  4. #4
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    Okay, but which part is the F(x,y)?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by clockingly View Post
    Okay, but which part is the F(x,y)?
    for the first one
    F(x,y) = (x^3)/3y differentiate this to check it
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