Example 41 - If y = sin-1 x, show that (1 - x2) d2y/dx2 - Finding second order derivatives- Implicit form

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Example 41 If y = 1 , show that (1 2) 2 2 = 0 . We have = 1 Differentiating . . . = 1 = 1 1 2 = Now, = 1 2 1 2 Again Differentiating . . . = 1 2 1 2 2 2 = 1 2 1 2 1 2 1 . 1 2 2 2 = 1 2 1 2 3 2 . (1) ( 2 ) 2 2 = 1 2 1 2 3 2 . 0 2 2 2 = 1 2 1 2 3 2 . 2 = Now, we need to prove 1 2 2 2 . = 0 Solving LHS 1 2 2 2 . = 1 2 . 1 2 3 2 1 2 1 2 = 1 2 1+ 3 2 1 2 1 2 = 1 2 1 2 1 2 1 2 = 0 = RHS Hence proved .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.