{"id":29922,"date":"2022-03-29T12:00:31","date_gmt":"2022-03-29T06:30:31","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=29922"},"modified":"2022-03-29T12:25:15","modified_gmt":"2022-03-29T06:55:15","slug":"ncert-solutions-for-class-12-maths-chapter-5-ex-5-4","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-4\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 5 Continuity and Differentiability Ex 5.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-4\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4<\/h2>\n

\"NCERT<\/p>\n

Ex 5.4 Class 12 NCERT Solutions Question 1.<\/strong>
\n\\(\\frac { { e }^{ x } }{ sinx } \\)
\nSolution:
\n\\(y=\\frac { { e }^{ x } }{ sinx } \\)
\n\\(for\\quad y=\\frac { u }{ v } ,\\)
\n\\(\\frac { dy }{ dx } =\\frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x } \\)
\n\\(or\\frac { dy }{ dx } =\\frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x } ,where\\quad x\\neq n\\pi ,x\\in z \\)<\/p>\n

Exercise 5.4 Class 12 Maths NCERT Solutions Question 2.<\/strong>
\n\\({ e }^{ { sin }^{ -1 }x }\\)
\nSolution:
\n\"Ex<\/p>\n

Question 3.
\n\\({ e }^{ { x }^{ 3 } }\\) = y
\nSolution:
\nLet y = \\({ e }^{ { x }^{ 3 } }\\)
\nDifferentiating w.r.t. x,
\n\\(\\frac{d y}{d x}=\\frac{d}{d x}\\left(e^{x^{3}}\\right)\\) = \\(e^{x^{3}} \\cdot \\frac{d}{d x}\\left(x^{3}\\right)\\)
\n= \\({ e }^{ { x }^{ 3 } }\\).3x\u00b2 = 3x\u00b2\\({ e }^{ { x }^{ 3 } }\\)<\/p>\n

\"NCERT<\/p>\n

Question 4.
\n\\(sin\\left( { tan }^{ -1 }{ e }^{ -x } \\right)\\) = y
\nSolution:
\n\\(sin\\left( { tan }^{ -1 }{ e }^{ -x } \\right)\\) = y
\n\\(\\frac { dy }{ dx } =cos\\left( { tan }^{ -1 }{ e }^{ -x } \\right) \\frac { d }{ dx } \\left( { tan }^{ -1 }{ e }^{ -x } \\right) \\)
\n\\(=cos\\left( { tan }^{ -1 }{ e }^{ -x } \\right) \\frac { 1 }{ 1+{ e }^{ -2x } } \\frac { d }{ dx } \\left( { e }^{ -x } \\right) \\)
\n\\(=-cos\\left( { tan }^{ -1 }{ e }^{ -x } \\right) \\frac { 1 }{ 1+{ e }^{ -2x } } .\\left( { e }^{ -x } \\right) \\)<\/p>\n

Question 5.
\n\\(log(cos\\quad { e }^{ x })\\) = y
\nSolution:
\n\\(\\frac { dy }{ dx } =\\frac { 1 }{ cos\\quad { e }^{ x } } \\left( -sin{ e }^{ x } \\right) .{ e }^{ x }\\quad =-tan\\left( { e }^{ x } \\right) \\)<\/p>\n

Question 6.
\n\\({ e }^{ x }+{ e }^{ { x }^{ 2 } }+\\)…\\(+{ e }^{ { x }^{ 5 } }\\) = y(say)
\nSolution:
\n\"Exercise<\/p>\n

Question 7.
\n\\(\\sqrt { { e }^{ \\sqrt { x } } }\\), x > 0
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 8.
\nlog(log x), x > 1
\nSolution:
\ny = log(log x), x > 1
\nDifferentiating w.r.t. x,
\n\\(\\frac{d y}{d x}\\) = \\(\\frac{1}{\\log x} \\cdot \\frac{d}{d x}\\)(log x)
\n= \\(\\frac{1}{\\log x} \\cdot \\frac{1}{x}\\) = \\(\\frac{1}{x \\log x}\\), x > 1<\/p>\n

Question 9.
\n\\(\\frac { cosx }{ logx }\\) = y(say),x>0
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 10.
\ncos(log x + ex), x > 0
\nSolution:
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-4\/ NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4 Ex 5.4 Class 12 NCERT Solutions Question 1. Solution: Exercise 5.4 Class 12 Maths NCERT Solutions …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-4\/ NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4 Ex 5.4 Class 12 NCERT Solutions Question 1. 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