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Find the Conservative vector field for the potential function by finding its gradient.

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Find the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Conservative vector field for the potential function by finding its gradient.

asked Feb 18, 2015 in CALCULUS by anonymous
reshown Feb 18, 2015 by goushi

1 Answer

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Step 1:

The potential function is image.

Gradient field :

If image is scalar function of two variables, then the gradient vector and it is denoted by image is image.

The gradient of the function image is image.

image is the partial derivative of image with respect to image.

Then image.

image is the partial derivative of image with respect to image.

Then image.

image

The conservative vector field is image.

Solution :

The gradient of image is image.

The conservative vector field is image.

answered Feb 21, 2015 by joseph Apprentice

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