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Math Help - Differentiable Mappings

  1. #1
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    Differentiable Mappings

    I am having trouble solving this question. I know you are supposed to use the limit defnition, but I can't figure it out.

    Let F: R^n -> R^m be a differentiable mapping. Given u, v are vectors in R^n, show that
    D_(au+bv)F = aD_u(F) + bD_v(F), where a, b: Rn -> R are arbitrary functions.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Use that D_uF(x)=F'(x)u where F'(x)\in\mathbb{R}^{m\times n} is the jacobian matrix of F at x .
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