Exercise 5.3 Class 12 Maths Ncert Solutions In Hindi Question 2.<\/strong> \n2x + 3y = siny \nSolution: \n2x + 3y = siny \nDifferentiating w.r.t x, \n\\(2+3.\\frac { dy }{ dx } =cosy\\frac { dy }{ dx } \\) \n\u21d2 \\(\\frac { dy }{ dx } =\\frac { 2 }{ cosy-3 } \\)<\/p>\n <\/p>\n
Question 3. \nax + by\u00b2 = cosy \nSolution: \nax + by\u00b2 = cosy \nDifferentiate both sides w.r.t. x, \n <\/p>\n
Question 4. \nxy + y\u00b2 = tan x + y \nSolution: \nxy + y\u00b2 = tan x + y \nDifferentiate both sides w.r.t. x, \n <\/p>\n
Question 5. \nx\u00b2 + xy + y\u00b2 = 100 \nSolution: \nx\u00b2 + xy + y\u00b2 = 100 \nDifferentiate both sides w.r.t. x, \n <\/p>\n
<\/p>\n
Question 6. \nx\u00b3 + x\u00b2y + xy\u00b2 + y\u00b3 = 81 \nSolution: \nx\u00b3 + x\u00b2y + xy\u00b2 + y\u00b3 = 81 \nDifferentiate both sides w.r.t. x, \n <\/p>\n
Question 7. \nsin\u00b2 y + cos xy = \u03c0 \nSolution: \nsin\u00b2 y + cos xy = \u03c0 \nDifferentiate both sides w.r.t. x, \n <\/p>\n
<\/p>\n
Question 8. \nsin\u00b2x + cos\u00b2y = 1 \nSolution: \nGiven that \nsin\u00b2x + cos\u00b2y = 1 \nDifferentiating both sides, we get \n <\/p>\n
Question 9. \ny = \\({ sin }^{ -1 }\\left( \\frac { 2x }{ { 1+x }^{ 2 } } \\right)\\) \nSolution: \n <\/p>\n
<\/p>\n
Question 10. \ny = \\({ tan }^{ -1 }\\left( \\frac { { 3x-x }^{ 3 } }{ { 1-3x }^{ 2 } } \\right) ,-\\frac { 1 }{ \\sqrt { 3 } } <x<\\frac { 1 }{ \\sqrt { 3 } } \\) \nSolution: \n <\/p>\n
Question 11. \ny = \\({ cos }^{ -1 }\\left( \\frac { 1-{ x }^{ 2 } }{ 1+{ x }^{ 2 } } \\right) ,0<x<1\\) \nSolution: \ny = \\({ cos }^{ -1 }\\left( \\frac { 1-{ x }^{ 2 } }{ 1+{ x }^{ 2 } } \\right) ,0<x<1\\) \nput x = tan\u03b8 \ny = \\({ cos }^{ -1 }\\left( \\frac { 1-tan^{ 2 }\\quad \\theta }{ 1+{ tan }^{ 2 }\\quad \\theta } \\right) ={ cos }^{ -1 }(cos2\\theta )=2\\theta\\) \n= 2\u03b8 = 2 tan-1 x \n<\/sup>i.e., y = 2 tan-1x \n<\/sup>Differentiating w.r.t x, \\(\\frac{d y}{d x}=\\frac{2}{1+x^{2}}\\)<\/p>\n <\/p>\n
Question 12. \ny = \\({ sin }^{ -1 }\\left( \\frac { 1-{ x }^{ 2 } }{ 1+{ x }^{ 2 } } \\right) ,0<x<1\\) \nSolution: \n <\/p>\n
Question 13. \ny = \\({ cos }^{ -1 }\\left( \\frac { 2x }{ 1+{ x }^{ 2 } } \\right)\\), – 1 < x < 1 \nSolution: \n <\/p>\n
<\/p>\n
Question 14. \ny = \\(sin^{ -1 }\\left( 2x\\sqrt { 1-{ x }^{ 2 } } \\right) ,-\\frac { 1 }{ \\sqrt { 2 } } <x<\\frac { 1 }{ \\sqrt { 2 } } \\) \nSolution: \n <\/p>\n
Question 15. \ny = \\(sin^{ -1 }\\left( \\frac { 1 }{ { 2x }^{ 2 }-1 } \\right) ,0<x<\\frac { 1 }{ \\sqrt { 2 } } \\) \nSolution: \ny = \\(sin^{ -1 }\\left( \\frac { 1 }{ { 2x }^{ 2 }-1 } \\right) ,0<x<\\frac { 1 }{ \\sqrt { 2 } } \\) \nput x = tan\u03b8 \nwe get \ny = \\(sec^{ -1 }\\left( \\frac { 1 }{ { 2cos }^{ 2 }\\theta -1 } \\right) ={ sec }^{ -1 }\\left( \\frac { 1 }{ cos2\\theta } \\right) \\) \ny = \\(sec^{ -1 }(sec2\\theta )=2\\theta ,\\quad 2{ cos }^{ -1 }x \\) \ni.e., y = 2 cos-1\u00a0<\/sup>x \nDifferentiating w.r.t.x, \n\u2234 \\(\\frac{d y}{d x}=\\frac{-2}{\\sqrt{1-x^{2}}}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"These NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.3 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-5-ex-5-3\/ NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.3 Ex 5.3 Class 12 NCERT Solutions Question 1. 2x + 3y = sinx Solution: 2x + …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.3<\/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 5.3 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n