TheoremIf f is a differentiable function of x andY,andand Ū:= cos î+ sin 0 ĵ, thencosD7f(x, y) = f(x, y) cos 0 + fy(x, y) sin 0.EXERCISE 2Consider f(x,y)3x2- 4y² andU = cos n î + sin ĵ.Use the Theorem above to find thedirectional derivative of f in the directionof the U.

Answered: Image /qna-images/answer/da4fbfb0-59fe-4a4b-8eeb-4d0a956118f1.jpg

Answered: EXERCISE 2 Consider f(x, y) 3x2 · 4y²…

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 function at P0 in the direction of u. 1.g(x, y, z) = 3ex cos yz, P0(0, 0, 0), u = 2i + j - 2k 2. h(x, y, z) = cos xy + eyz + ln zx, P0(1, 0, 1/2), u = i + 2j + 2k
Let x and y be differentiable functions of t and lets = sqrt(x2 + y2) be the distance between the points (x, 0) and(0, y) in the xy-plane.a. How is ds/dt related to dx/dt if y is constant?b. How is ds/dt related to dx/dt and dy/dt if neither x nor y isconstant?c. How is dx/dt related to dy/dt if s is constant?
Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎ co‎ntinuous at (0,‎ 0)
A differentiable function f(x,y) has the property that f(2,4)=2 and fx(2,4)=5 and fy(2,4)=−6. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=2, y=4. z=?
Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0) and (1,2) with positive orientation. (b) Compute the directional derivative of the function f(x, y, z) = xy2 + y2z3 + z3x at the point P(4, -2, -1) in the direction of Q(l, 3, 2)
Use Theorem 12.33 to find the indicated derivatives in Exercises27–30. Express your answers as functions of twovariables. 27. ∂z/∂s when z = x2y3, x = t sin s, and y = s cos t.28. ∂z/∂t when z = x2y3, x = t sin s, and y = s cos t.29. ∂z/∂r when z = (x2 + xy)ey, x = r cos θ, and y = r sin θ.30. ∂z/∂θ when z = (x2 + xy)ey, x = r cos θ, and y = r sin θ.
Suppose that f(x, y, z) = x^2 + y^2 + z^2 + 3xyz. A. Find the directional derivative of f(x, y, z) at (1, 1, 1) in the direction of v = 2i − 2j + k. B. Find the direction in which f(x, y, z) is increasing most rapidly at the point (1, 1, 1), and the magnitude of the rate of increase in that direction. C. Find an equation of the tangent plane to the surface x^2 +y^2 +z^2 + 3xyz = 6 at the point (1, 1, 1).
Let x and y be differentiable functions of t and let s = 2x2 + y2 be the distance between the points (x, 0) and (0, y) in the xy-plane. a. How is ds/dt related to dx/dt if y is constant? b. How is ds/dt related to dx/dt and dy/dt if neither x nor y is constant? c. How is dx/dt related to dy/dt if s is constant?

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

EXERCISE 2 Consider f(x, y) 3x2 · 4y² and U = cos r î + sin r ĵ. Use the Theorem above to find the directional derivative of f in the direction of the Ū.