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Math Help - Second partials

  1. #1
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    Second partials

    Find second partials ( f_{vv} and f_{uv}):

    f(u, v) = 5ln(u^2 + v^2)

    f_{v} = \frac{10v}{u^2 + v^2}

    f_{vu} = -1(u^2 + v^2)^{-2}(2u)10v

    f_{vu} = - \frac{20uv}{(u^2 + v^2)^2}

    the correct answer is f_{uv} = - \frac {40uv}{(u^2 + v^2)^2}

    Where did I go wrong finding f_{uv}?
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  2. #2
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    Quote Originally Posted by Macleef View Post
    Find second partials ( f_{vv} and f_{uv}):

    f(u, v) = 5ln(u^2 + v^2)

    f_{v} = \frac{10v}{u^2 + v^2}

    f_{vu} = -1(u^2 + v^2)^{-2}(2u)10v

    f_{vu} = - \frac{20uv}{(u^2 + v^2)^2}

    the correct answer is f_{uv} = - \frac {40uv}{(u^2 + v^2)^2}

    Where did I go wrong finding f_{uv}?
    Hi

    f_{v} = \frac{10v}{u^2 + v^2}

    f_{vu} = \frac{\partial}{\partial u} \left(\frac{10v}{u^2 + v^2}\right) = -\frac{20uv}{(u^2 + v^2)^2}

    I agree with your answer
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