Chapter 16.1, Problem 21E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the gradient vector field of *f*.

**21.** *f*(*x*, *y*) = *y* sin(*xy*)

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.

Write the required differentiation formulae as follows.

Differentiate terms with respect to

Differentiate terms with respect to

Find the gradient vector field of

Modify equation (1) as follows.

Modify equation (2) as follows.

Differentiate and rewrite the equation as follows.

Modify equation (2) as follows

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