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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

(a) Find the gradient of f.

(b) Evaluate the gradient at the point P.

(c) Find the rate of change of f at P in the direction of the vector u.

8. f(x, y) = x2 ln y, P(3, 1), u = − 5 13 i + 12 13 j

(a)

To determine

To find: The gradient of f(x,y)=x2lny .

Explanation

Calculation:

The given function is, f(x,y)=x2lny .

The gradient of f(x,y) is computed as follows,

f(x,y)=fxi+fyj=x(x2lny)i+y(x2lny)</

(b)

To determine

To evaluate: The gradient of f(x,y)=x2lny at the point P(3,1) .

(c)

To determine

To find: The rate of change of f(x,y)=x2lny at the point (3,1) and in the direction of the vector, u=513i+1213j .

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Chapter 14 Solutions

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