   Chapter 15.1, Problem 44E ### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

#### Solutions

Chapter
Section ### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Determine whether the vector field is conservative. If it is, find a potential function for the vector field. F ( x , y ) = ( ln y + 2 ) i ^ + x y j ^ .

To determine

Whether the vector field is conservative F(x,y) = (lny+2)i^+xyj^.. If it is, find a potentialfunction for the vector field.

Explanation

Given: The function F(x,y) = (lny+2)i^+xyj^.

A vector field F(x,y) = Mi^+Nj^ is said to be conservative if and only if

My=Nx, where M and N are differentiable functions.

Here, M=siny

Now, partial differentiating both sides with respect to ‘y’

=>My=y(lny+2)

=(ylny+y2)

=1y

and, N=xcosy

Now, partial differentiating both sides with respect to ‘x’

=>Nx=x(xy)

=1yx(x)

=1y

Clearly, My=Nx

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