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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    I was wondering if someone could help me out.
    I was given the function f(x,y)=squareroot(1+ x^2 + y^2) and asked to find the slope of a tangent to a level curve at point (-2,2).

    I have managed to work out the gradient of f at (-2,2) to be (-2/3, 2/3), and I know it has to be orthogonal to the tangent, but I am unsure as to how to work out the slope of the tangent.

    Would appreciate your help
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  2. #2
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    Quote Originally Posted by Pandora View Post
    I was wondering if someone could help me out.
    I was given the function f(x,y)=squareroot(1+ x^2 + y^2) and asked to find the slope of a tangent to a level curve at point (-2,2).

    I have managed to work out the gradient of f at (-2,2) to be (-2/3, 2/3), and I know it has to be orthogonal to the tangent, but I am unsure as to how to work out the slope of the tangent.

    Would appreciate your help
    \frac{dy}{dx}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}
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  3. #3
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    Thank you. Would you mind working it out from the facts? I am pretty horrible at implicit differentiation.
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  4. #4
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    Quote Originally Posted by Pandora View Post
    Thank you. Would you mind working it out from the facts? I am pretty horrible at implicit differentiation.
    \frac{\partial F}{\partial x}=\frac{x}{\sqrt{1+x^2+y^2}}

    \frac{\partial F}{\partial y}=\frac{y}{\sqrt{1+x^2+y^2}}

    \frac{dy}{dx}=-\frac{\frac{x}{\sqrt{1+x^2+y^2}}}{\frac{y}{\sqrt{1  +x^2+y^2}}}

    Now simplify and solve.
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