Explanation Given information: f ( x , y , z ) = sin ( x y + z ) , P = ( 0 , − 1 , π ) Calculation: Since the gradient of function is denoted by ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z 〉 The given equation f ( x , y , z ) = sin ( x y + z ) , Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x sin ( x y + z ) ⇒ ∂ f ∂ x = [ cos ( x y + z ) ] ( ∂ ∂ x ( x y + z ) ) ⇒ ∂ f ∂ x = [ cos ( x y + z ) ] ( y + 0 ) = y cos ( x y + z ) Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y sin ( x y + z ) ⇒ ∂ f ∂ y = cos ( x y + z ) ∂ ∂ y ( x y + z ) = cos ( x y + z ) ( x + 0 ) = x cos ( x y + z ) Differentiating f with respect to z we get, ∂ f ∂ z = ∂ ∂ z sin ( x y + z ) ⇒ ∂ f ∂ z = cos ( x y + z )<

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

See similar textbooks

Concept explainers

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic…

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along…

Triple Integral

Examples:

Videos

Question

Chapter 14.5, Problem 39E

To determine

Tocalculate:

Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 38E

Chapter 14.5, Problem 40E

Students have asked these similar questions

3. Consider the initial value problem 9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1. Solve the problem and find the value of a such that the solution of the initial value problem is always positive.

5. Euler's equation. Determine the values of a for which all solutions of the equation 5 x²y" + axy' + y = 0 that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.

4. Problem on variable change. The purpose of this problem is to perform an appropriate change of variables in order to reduce the problem to a second-order equation with constant coefficients. ty" + (t² − 1)y'′ + t³y = 0, 0

Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Tocalculate: D u f ( P ) where u is a unit vector making an angle θ = 30 o with ∇ f p

Solution Summary: The author explains that d_uf(P) is a unit vector making an angle.

Concept explainers

Videos

Tocalculate:

Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

Want to see the full answer?

Chapter 14 Solutions

Tocalculate: D u f ( P ) where u is a unit vector making an angle θ = 30 o with ∇ f p

Solution Summary: The author explains that d_uf(P) is a unit vector making an angle.

Concept explainers

Videos

Tocalculate: Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

Want to see the full answer?

Chapter 14 Solutions

Tocalculate:

Duf(P) where u is a unit vector making an angle θ=30o with ∇fp