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Math Help - Differentiable function

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    Differentiable function

    By using the definition of a differentiable function, show that the following function is differentiable in (2,2):

    f(x,y) = e^[x + 2y]

    Thx!!
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  2. #2
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    Re: Differentiable function

    Quote Originally Posted by marqushogas View Post
    By using the definition of a differentiable function, show that the following function is differentiable in (2,2):

    f(x,y) = e^[x + 2y]

    Thx!!
    Well, what is the definition of differentiability?
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  3. #3
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    Re: Differentiable function

    In two variables: If a function f(x,y) is differentiable in (a,b) there exists two numbers, A and B, and a function r(h,k) such that:

    f(a+h,b+k) - f(a,b) = A*h + B*k + sqrt(h^2+k^2)*r(h,k) and r(h,k) -> 0 when (h,k) -> (0,0)
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