Chapter 16.3, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Determine whether or not **F** is a conservative vector field. If it is, find a function *f* such that **F** = ∇* f*.

**8. F**(*x*, *y*) = (2*xy* + *y*^{−2}) **i** + (*x*^{2} − 2*xy*^{−3}) **j**, *y* > 0

To determine

Whether
*f* such that

Explanation

**Given data:**

Vector field is

**Formula used:**

Consider a vector field as

Here,

*P*, and

*Q*,

Compare the vector field

Apply partial differentiation with respect to *y* on both sides of equation (2).

Apply partial differentiation with respect to *x* on both sides of equation (3).

Substitute

Hence

Consider

Write the relation between the potential function *f* and vector field

Substitute

Compare the equation

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