Chapter 16.1, Problem 25E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the gradient vector field ∇*f* of* f* and sketch it.

**25.** *f*(*x*, *y*) =
*x − y*)^{2}

To determine

**To find:** The gradient vector field for equation

Explanation

**Given data**:

**Formula used:**

Write the expression for gradient vector field of two dimensional vector.

Consider a two-dimensional vector

Write the expression for length of the two dimensional vector.

Write the required differentiation formulae with respect to

Write the required differentiation formulae with respect to

Differentiate the term

Differentiate the term

Find the gradient vector field of

Modify equation (1) as follows.

Substitute

Thus, the gradient vector field for

Find the length of

Consider a certain interval of *x* as
*y* as

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