{"id":4643,"date":"2023-12-21T10:34:26","date_gmt":"2023-12-21T05:04:26","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4643"},"modified":"2023-12-22T17:22:15","modified_gmt":"2023-12-22T11:52:15","slug":"samacheer-kalvi-12th-maths-solutions-chapter-8-ex-8-6","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-8-ex-8-6\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.6"},"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 8.6<\/h2>\n

Question 1.
\nIf u(x, y) = x2<\/sup>y + 3xy4<\/sup>, x = et<\/sup> and y = sin t, find \\(\\frac{d u}{d t}\\) and evaluate it at t = 0.
\nSolution:
\n\"Samacheer
\n= (2xy + 3y4<\/sup>) (et<\/sup>) + (x2<\/sup> + 12xy3<\/sup>) (cos t)
\n= (2et<\/sup> sin t + 3 sin4<\/sup> t) et<\/sup> + [e2t<\/sup> + 12et<\/sup> sin3<\/sup> t] cos t
\n= et<\/sup> [2et<\/sup> sin t + 3 sin4<\/sup> t + et<\/sup> (cos t) + 12 sin3<\/sup>t cos t]
\nat t = 0
\n\"Samacheer<\/p>\n

Question 2.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nIf w(x, y, z) = x2<\/sup> + y2<\/sup> + z2<\/sup>, x = et<\/sup>, y = et<\/sup> sin t, and z = et<\/sup>cos t, find \\(\\frac{d w}{d t}\\)
\nSolution:
\nw(x, y, z) = x2<\/sup> + y2<\/sup> + z2<\/sup> ; x = et<\/sup> ; y = et<\/sup> sin t, z = et<\/sup> cos t
\n\"Samacheer<\/p>\n

Question 4.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n(Replace x, y, z value)
\n\"Samacheer<\/p>\n

Question 5.
\nIf w(x, y) = 6x3<\/sup> – 3xy + 2y2<\/sup>, x = es<\/sup>, y = cos s, s \u2208 R, find \\(\\frac{d w}{d s}\\), and evaluate at s = 0.
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nIf z(x, y) = x tan-1<\/sup> (x y), x = t2<\/sup>, y = s et<\/sup>, s, t \u2208 R, Find \\(\\frac{\\partial z}{\\partial \\mathbf{t}}\\) and \\(\\frac{\\partial z}{\\partial \\mathbf{t}}\\) at s = t = 1
\nSolution:
\nz (x, y) = x tan-1<\/sup> (xy) ; x = t2<\/sup> ; y = set<\/sup>
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 7.
\nLet U (x, y) = ex<\/sup> sin y, where x = st2<\/sup>, y = s2<\/sup>t, s, t \u2208 R. Find them at s = t = 1.
\nSolution:
\n\"Samacheer
\n(Replace x, y values)
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 8.
\nLet z(x, y) = x3<\/sup> – 3x2<\/sup>y3<\/sup>, where x = set<\/sup>, y = se-t<\/sup>, s, t \u2208 R. Find \\(\\frac{\\partial z}{\\partial s}\\) and \\(\\frac{\\partial z}{\\partial t}\\)
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 9.
\nW(x,y, z) = xy + yz + zx, x = u -v, y = uv, z = u + v, u, v e R. Find \\(\\frac{\\partial \\boldsymbol{w}}{\\partial \\boldsymbol{u}}\\), \\(\\frac{\\partial \\boldsymbol{w}}{\\partial \\boldsymbol{v}}\\) them at \\(\\left(\\frac{1}{2}, 1\\right)\\)
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Samacheer Kalvi 12th Maths Solutions Chapter 8 Differentials and Partial Derivatives Ex 8.6 Additional Problems<\/h3>\n

Question 1.
\nSuppose that z = \\(y e^{x^{2}}\\) where x = 2t and y = 1 – t then find \\(\\frac{d z}{d t}\\).
\nSolution:
\n\"Samacheer
\n\"Samacheer
\n(Since x = 2t and y = 1 – t)<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf w = x + 2y + z2<\/sup> and x = cos t ; y = sin t ; z = t. Find \\(\\frac{d w}{d t}\\).
\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 8.6 Question 1. If u(x, y) = x2y + 3xy4, x = et and y = …<\/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\/4643"}],"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=4643"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4643\/revisions"}],"predecessor-version":[{"id":60212,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4643\/revisions\/60212"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=4643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=4643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=4643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}