   Chapter 15, Problem 6RE ### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

#### Solutions

Chapter
Section ### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding a Conservative Vector Field In Exercises 3-6, find the conservative vector field for the potential function by finding its gradient. f ( x , y , z ) = x 2 e y z

To determine

To calculate: The conservative vector field for the potential function f(x,y,z)=x2eyz.

Explanation

Given:

The potential function is: f(x,y,z)=x2eyz

Formula used:

The conservative vector field for the potential function f(x,y,z) is given by,

f(x,y)=fxi^+fyj^+fzk^

Chain rule,

xf(g(x))=f(x)xg(x)

Calculation:

In order to compute the vector field for the provided potential function f(x,y), first find the gradient of the function f.

Since F(x,y,z)=f.

Now,

f(x,y)=fxi^+fyj^+fzk^

Substitute the value of the function f(x,y,z)=x2eyz in above formula, to get,

f(x,y,z)=x(x2eyz)i^+y(x2eyz)j

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