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Math Help - derivative matrix

  1. #1
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    derivative matrix

    I need to compute the derivative matrix for

    f(x,y) = (xe^y + cos(y), x , x+e^y)

    would this be f : \mathbb{R}^2 \to \mathbb{R}^3 making a 3x2 matrix ??
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  2. #2
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    Re: derivative matrix

    Yes

    \begin{pmatrix}\tfrac{\partial (xe^y + \cos y)}{\partial x} & \tfrac{\partial (xe^y + \cos y)}{\partial y} \\ \tfrac{\partial (x)}{\partial x} & \tfrac{\partial (x)}{\partial y} \\ \tfrac{\partial(x+e^y)}{\partial x}  & \tfrac{\partial(x+e^y)}{\partial y}\end{pmatrix}

    Note: By "derivative matrix", I assume you are looking for the Jacobian. There could be other derivative matrices (in theory).
    Last edited by SlipEternal; June 27th 2014 at 08:39 PM.
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  3. #3
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    Re: derivative matrix

    Quote Originally Posted by SlipEternal View Post
    Yes

    \begin{pmatrix}\tfrac{\partial (xe^y + \cos y)}{\partial x} & \tfrac{\partial (xe^y + \cos y)}{\partial y} \\ \tfrac{\partial (x)}{\partial x} & \tfrac{\partial (x)}{\partial y} \\ \tfrac{\partial(x+e^y)}{\partial x}  & \tfrac{\partial(x+e^y)}{\partial y}\end{pmatrix}

    Note: By "derivative matrix", I assume you are looking for the Jacobian. There could be other derivative matrices (in theory).
    yeah the jacobian

    thanks
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  4. #4
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    Re: derivative matrix

    This is exactly the same as in your thread
    linear approximation of mapping
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