   Chapter 14.6, Problem 8E

Chapter
Section
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 .

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

CHECK POINT 2. (a) W rite as radicals. (b)Write with fractional exponents:

Mathematical Applications for the Management, Life, and Social Sciences

Given the tangents with m3=46, find: a mRST b mRT

Elementary Geometry For College Students, 7e

Use graphing to solve {2x+y=5x2y=0.

College Algebra (MindTap Course List) 