For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y²; P (7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan (²)
For each problem, calculate the directional derivative in the given direction and the gradient vector: 11. z = x² - 6y²; P (7,2); a) 0 = 45°; b) 0 = 135° 12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120° 13. z = x² + xy + y²; P (3,1); 0 = 14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan (²)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
Related questions
Question
pls solve all
do not provide solution in image format thank you!
![Directional Derivative and Gradient Vector
For each problem, calculate the directional derivative in the given direction and the gradient vector:
11. z = x² - 6y2; P(7,2); a) 0 = 45°; b) 0 = 135°
12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120°
13. z = x² + xy + y²; P (3,1); 0 =
14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan
NIM](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b4ab23-f6d5-4206-a94e-63cad8267fd4%2F4c3bcfce-3c59-4c90-b873-aea2b466b375%2Fz5j9sqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Directional Derivative and Gradient Vector
For each problem, calculate the directional derivative in the given direction and the gradient vector:
11. z = x² - 6y2; P(7,2); a) 0 = 45°; b) 0 = 135°
12. z = ye*; P(0,3); a) 0 = 30°; b) 0 = 120°
13. z = x² + xy + y²; P (3,1); 0 =
14. z = x3 + y3 – 3xy; P(2,1); 0 = arctan
NIM
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Algebra and Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning