{"id":4617,"date":"2023-12-20T09:18:32","date_gmt":"2023-12-20T03:48:32","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4617"},"modified":"2023-12-21T17:51:38","modified_gmt":"2023-12-21T12:21:38","slug":"samacheer-kalvi-12th-maths-solutions-chapter-8-ex-8-4","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-8-ex-8-4\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.4"},"content":{"rendered":"

You can Download\u00a0<\/span>Samacheer Kalvi 12th Maths Book Solutions<\/a>\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/span><\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.4<\/h2>\n

Question 1.
\nFind the partial derivatives of the following functions at the indicated points.
\n(i) f(x, y) = 3x2<\/sup> – 2xy + y2<\/sup> + 5x + 2, (2, -5)
\n(ii) g(x, y) = 3x2<\/sup> + y2<\/sup> + 5x + 2, (1, -2)
\n\"Samacheer
\n(iv) G (x, y) = e*x + 3y<\/sup> log (x2<\/sup> + y2<\/sup>), (-1, 1)
\nSolution:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nFor each of the following functions find the fx<\/sub>, fy<\/sub> and show that fxy<\/sub> = fyx<\/sub>
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 5.
\nFor each of the following functions find the gxy<\/sub>, gxx<\/sub>, gyy<\/sub> and gyx<\/sub>.
\n(i) g(x, y) = xey<\/sub> + 3x2<\/sub>y
\n(ii) g(x, y) = log(5x + 3y)
\n(iii) g(x, y) = x2<\/sub> + 3xy – 7y + cos(5x)
\nSolution:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 7.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 9.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 10.
\nA firm produces two types of calculators each week, x number of type A and j number of type B . The weekly revenue and cost functions (in rupees) are
\nR(x, y) = 80x + 90y + 0.04xy – 0.05.x2<\/sup> – 0.05y2<\/sup> and C(x, y) = 8x + 6y + 2000 respectively.
\n(i) Find the profit function P(x,y),
\n\"Samacheer
\nSolution:
\n(i) Profit = Revenue – Cost
\n= (80x + 90y + 0.04 xy – 0.05 x2<\/sup> – 0.05y2<\/sup>) – (8x + 6y + 2000)
\n= 80x + 90y + 0.04 xy – 0.05 x2<\/sup> – 0.05y2<\/sup> – 8x – 6y – 2000
\nP(x, y) = 72x + 84y + 0.04 xy – 0.05 x2<\/sup> – 0.05y2<\/sup> – 2000
\n\"Samacheer
\n\"Samacheer<\/p>\n

Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.4 Additional Problems<\/h3>\n

Question 1.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf U = (x – y) (y – z) (z – x) then show that Ux<\/sub> + Uy<\/sub> + Uz<\/sub> = 0
\nSolution:
\nUx<\/sub> = (y – z) {(x – y)(-1) + (z – x). 1}
\n= (y – z) [(z – x) – (x – y)]
\nSimilarly Uy<\/sub> = (z – x) [(x – y) – (y – z)]
\nz<\/sub> = (x – y)[(y – z) – (z – x]
\nUx<\/sub> + Uy<\/sub> + Uz<\/sub> = (y – z) [(z – x) – (z – x)] + (x – y) [- (y – z) + (y – z)] + (z – x) [(x – y) – (x – y)]
\n\u2234 Ux<\/sub> + Uy<\/sub> + Uz<\/sub> = 0.
\nHence proved.<\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download\u00a0Samacheer Kalvi 12th Maths Book Solutions\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.4 Question 1. Find the partial derivatives of the following functions at the indicated points. (i) …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4617"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=4617"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4617\/revisions"}],"predecessor-version":[{"id":60191,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4617\/revisions\/60191"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=4617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=4617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=4617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}