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Math Help - Find gradient vector

  1. #1
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    Find gradient vector

    Don't know how to do this. Please help!!
    Find gradient vector of f(x,y).
    Attached Thumbnails Attached Thumbnails Find gradient vector-05052008.jpg  
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  2. #2
    Moo
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    Hello,

    f(x,y)=\sqrt{\frac{x+y}{x-y}}

    The gradient vector of a function is defined as following :

    \vec{\nabla}f=\left(\frac{\partial f}{\partial x} \ , \ \frac{\partial f}{\partial y} \right)

    For example, \frac{\partial f}{\partial x} is the derivative of f, considering that x is the variable and y is a constant.
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  3. #3
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    This is what I just worked out ( 2y/(x-y)^2 , -2y/(x-y)^2 ), not sure if that's the answer?
    Please help!
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    Quote Originally Posted by Moo View Post
    f(x,y)=\sqrt{\frac{x+y}{x-y}}
    Quote Originally Posted by 4sweet2005 View Post
    This is what I just worked out ( 2y/(x-y)^2 , -2y/(x-y)^2 ), not sure if that's the answer?
    Please help!
    \frac{\partial }{\partial x} \left ( \sqrt{\frac{x+y}{x-y}} \right )

    = \frac{1}{2} \cdot \frac{1}{\sqrt{\frac{x+y}{x-y}}} \cdot \left ( \frac{(1)(x - y) - (x + y)(1)}{(x - y)^2} \right )

    = \sqrt{\frac{x-y}{x+y}} \cdot \left ( \frac{-2y}{2(x - y)^2} \right )

    = -\frac{y}{(x - y)^{3/2} (x + y)^{1/2}}

    Try your y derivative again.

    -Dan
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