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Math Help - Need help with implicit differentiation

  1. #1
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    Need help with implicit differentiation

    sqrt(5xy) + 2y = y^2 + xy^3

    so I got this far and now I am stuck:

    d/dx ((5xy)^1/2 + 2y) = d/dx (y^2 + xy^3)

    = 1/2(5xy)^1/2-1) Dx(5x) (y) + 5x Dx(y) + 2 Dx(y) = 2y Dx(y) + Dx(x) (y^3) + x (3y^2) Dx (y)

    = 1/(2sqrt(5xy)) 5y + 5x Dx(y) + 2 Dx(y) = 2y Dx(y) + y^3 +3xy^2 Dx(y)

    =?
    I'm wondering if I'm doing this right and where would I go from there?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    1/(2sqrt(5xy)) 5y + 5x Dx(y) + 2 Dx(y) = 2y Dx(y) + y^3 +3xy^2 Dx(y)


    The notation is a bit cumbersome but you did a good job

    See attachment
    Attached Thumbnails Attached Thumbnails Need help with implicit differentiation-implicit.jpg  
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