{ "key_pair_value_system": true, "answer_rating_count": "", "question_feedback_html": { "html_star": "", "html_star_feedback": "" }, "answer_average_rating_value": "", "answer_date_js": "2024-06-06T14:09:21-04:00", "answer_date": "2024-06-06 14:09:21", "is_docs_available": "", "is_excel_available": "", "is_pdf_available": "", "count_file_available": 0, "main_page": "student_question_view", "question_id": "2370648", "url": "\/study-help\/questions\/1-use-the-chain-rule-to-find-and-ay-2370648", "question_creation_date_js": "2024-06-06T14:09:21-04:00", "question_creation_date": "Jun 06, 2024 02:09 PM", "meta_title": "[Solved] 1. Use the chain rule to find . and ay ' | SolutionInn", "meta_description": "Answer of - 1. Use the chain rule to find . and ay ' for y'cos (5z - 2x) = 1 + esin(6zy). 2. Find the directional derivative of th | SolutionInn", "meta_keywords": "1,chain,rule,find,ay,y,cos,5z,-,2x,+,esin", "question_title_h1": "1. Use the chain rule to find . and ay ' for y'cos (5z - 2x) = 1 + esin(6zy). 2. Find the directional derivative", "question_title": "1. Use the chain rule to find . and ay ' for", "question_title_for_js_snippet": "1 Use the chain rule to find and ay ' for y'cos (5z 2x) 1 esin(6zy) 2 Find the directional derivative of the function f(x, y, 2) xtan '(y 2) at the point (2, 1, 1) in the direction of the vector v (1, 1, 1) 3 Use differentials to approximate the value of 8 94 9 99 (1 01)3 4 The dimensions of a closed rectangular box are measured as 80 cm, 60 cm and 50 cm respectively, with a possible error of 0 2 in each dimension Use differentials to calculate the maximum error in calculating the surface area of the box 5 Find the gradient of the function g(x, y) Invx2 y2 at (1, 2) 6 Find equations of the tangent plane and the normal line to the surface re 1 at the point (1, 0, 5) 7 Suppose you are climbing a hill whose shape is given by the equation z f(x, y) 1000 0 01x2 0 02y', where r, y, and z are measured in meters, and you are standing at a point P(60, 100, 764) (a) In which direction should you proceed initially in order to reach the top of the hill fastest (b) What is the maximum rate of ascent at P 8 Find the local maximum and minimum values and saddle points of the function (i) f(x,y) 3xy aly ry (ii) g(x, y) y' 2y cost, 1", "question_description": "\"image
\"image<\/div><\/div><\/div><\/figure> 1. Use the chain rule to find . and ay \"' for y'cos (5z - 2x) = 1 + esin(6zy). 2. Find the directional derivative of the function f(x, y, 2) = xtan-'(y\/2) at the point (2, 1, 1) in the direction of the vector v = (1, 1, 1). 3. Use differentials to approximate the value of 8.94\\\/9.99 - (1.01)3. 4. The dimensions of a closed rectangular box are measured as 80 cm, 60 cm and 50 cm respectively, with a possible error of 0.2 in each dimension. Use differentials to calculate the maximum error in calculating the surface area of the box. 5. Find the gradient of the function g(x, y) = Invx2 + y2 at (1, 2). 6. Find equations of the tangent plane and the normal line to the surface re = = 1 at the point (1, 0, 5). 7. Suppose you are climbing a hill whose shape is given by the equation z = f(x, y) = 1000-0.01x2-0.02y', where r, y, and z are measured in meters, and you are standing at a point P(60, 100, 764). (a) In which direction should you proceed initially in order to reach the top of the hill fastest? (b) What is the maximum rate of ascent at P? 8. Find the local maximum and minimum values and saddle points of the function. (i) f(x,y) = 3xy - aly - ry?. (ii) g(x, y) = y' - 2y cost, -1", "transcribed_text": "", "related_book": { "title": "Essentials Of Forensic Accounting", "isbn": "1948306441, 978-1948306447", "edition": "2nd Edition", "authors": "Michael A Crain, William S Hopwood", "cover_image": "https:\/\/dsd5zvtm8ll6.cloudfront.net\/si.question.images\/book_images\/2021\/11\/6180cb73a5085_6436180cb7324789.jpg", "uri": "\/textbooks\/essentials-of-forensic-accounting-2nd-edition-9-78e-12", "see_more_uri": "" }, "free_related_book": { "isbn": "9401038422", "uri": "\/textbooks\/recent-developments-in-infinite-dimensional-analysis-and-quantum-probability-papers-in-honour-of-takeyuki-hidas-70th-birthday-1st-edition-978-9401038423-351299", "name": "Recent Developments In Infinite Dimensional Analysis And Quantum Probability Papers In Honour Of Takeyuki Hidas 70th Birthday", "edition": "1st Edition" }, "question_posted": "2024-06-06 14:09:21", "see_more_questions_link": "\/study-help\/questions\/sciences-biology-2023-February-20", "step_by_step_answer": "The Answer is in the image, click to view ...", "students_also_viewed": [ { "url": "\/distinguish-between-expenditures-for-ordinary-repairs-and-extraordinary-repairs-expenditures", "description": "Distinguish between expenditures for ordinary repairs and extraordinary- repairs expenditures.", "stars": 3 }, { "url": "\/study-help\/human-resource-management\/efficiency-how-much-can-ihrm-help-make-the-mne-more-1659151", "description": "Efficiency (how much can IHRM help make the MNE more efficient by deliv ering the most effective human resources that will deliver world-class products and services worldwide?)", "stars": 3 }, { "url": "\/study-help\/biostatistics\/for-a-sample-of-88-observations-crossclassified-into-1981196", "description": "For a sample of ???? = 88 observations cross-classified into a 3 3 contingency table, how many degrees of freedom does the test statistic ????2 have in a test of independence?", "stars": 3 }, { "url": "\/jason-worked-various-jobs-during-his-teenage-years-to-save", "description": "Jason worked various jobs during his teenage years to save money for college. 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