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Math Help - Equality of two expressions involving derivatives.

  1. #1
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    Equality of two expressions involving derivatives.

    Can anybody please explain this?

    -u(\rho u)_{\eta} = -[(\rho u^{2})_{\eta} - (\rho u)u_{\eta}]

    When I use the product rule I get the right term but do not know where the left term comes from
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  2. #2
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    Quote Originally Posted by davefulton View Post
    Can anybody please explain this?

    -u(\rho u)_{\eta} = -[(\rho u^{2})_{\eta} - (\rho u)u_{\eta}]

    When I use the product rule I get the right term but do not know where the left term comes from
    Assuming the subscript denotes differentiation, the left hand side is -u^2 \rho_\eta - u \rho u_\eta.

    The right hand side can be written as -( [\rho_nu u^2 + \rho 2 u u_\eta] - u \rho u_\eta) which clearly simplifies to the left hand side.
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