Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the directionvector.f(x,y)= In (8+3x²+3y²); P(3,-1); (3,2)Find the gradient of f(x,y)= In (8+3x²+3y²).Vf(x,y) = (

Topic:- application of derivatives

Answered: tor. f(x,y)= In (8+3x²+3y²); P(3,-1);…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Find the derivative of the vector functionr(t)=ta×(b+tc), wherea=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and c=⟨−2,−4,−4⟩.r′(t)=⟨ , , ⟩
Find the directional derivative of the function f: R2→R, f (x, y)= xy2 + x2y in the direction of the vector v=(3,7)
Find the directional derivative of the function at the given point in the direction of the vector v. g(s,t)=st1/2, (2,4), v = <3, -1>
Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the vector 〈√3 , −1〉.
Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to:
find the directions in which ƒ increases and decreasesmost rapidly at P0 and find the derivative of ƒ in each direction.Also, find the derivative of ƒ at P0 in the direction of the vector v. ƒ(x, y, z) = ln (2x + 3y + 6z), P0(-1, -1, 1), v = 2i + 3j + 6k
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = x2y + y2z, (2, 7, 9), v = 2, −1, 2
Find the gradient of the function w = 1/(√1 − x2 − y2 − z2), and the maximum value of the directional derivative at the point (0, 0, 0).
Find the directional derivative Du f(−5/6,1) for the function f(x,y)=cos(π(3x+4y)) in the direction u parallel to the vector v=⟨9,12⟩.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=