Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 5

Advertisement

Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 6

Advertisement

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

Transcript

Example 44 Differentiate w.r.t. x, the following function: (ii) ๐‘’^(sec^2โก๐‘ฅ ) + 3cos^(โ€“1) ๐‘ฅ Let y = ๐‘’^(sec^2โก๐‘ฅ ) + 3cos^(โ€“1) ๐‘ฅ Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘‘(๐‘’^(sec^2โก๐‘ฅ )+ 3cos^(โ€“1) ๐‘ฅ" " )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘‘(๐‘’^(sec^2โก๐‘ฅ ) )/๐‘‘๐‘ฅ + ๐’…(๐Ÿ‘ใ€–๐’„๐’๐’”ใ€—^(โ€“๐Ÿ) ๐’™)/๐’…๐’™ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(sec^2โก๐‘ฅ ) ๐‘‘(sec^2โก๐‘ฅ )/๐‘‘๐‘ฅ + 3. ((โˆ’๐Ÿ)/โˆš(๐Ÿ โˆ’๐’™^๐Ÿ )) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(sec^2โก๐‘ฅ ). 2 sec ๐‘ฅ . ๐’…(ใ€–๐’”๐’†๐’„ ใ€—โก๐’™ )/๐’…๐’™ โˆ’ 3/โˆš(1 โˆ’๐‘ฅ^2 ) "As" ๐‘‘(๐‘’^๐‘ฅ )/๐‘‘๐‘ฅ=๐‘’^๐‘ฅ & ๐‘‘(ใ€–๐‘๐‘œ๐‘ ใ€—^(โˆ’1)โก๐‘ฅ )/๐‘‘๐‘ฅ=(โˆ’1)/โˆš(1 โˆ’ใ€– ๐‘ฅใ€—^2 ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(sec^2โก๐‘ฅ ). 2 sec ๐‘ฅ . ๐’”๐’†๐’„โก๐’™ .๐’•๐’‚๐’โก๐’™ โˆ’ 3/โˆš(1 โˆ’ ๐‘ฅ^2 ) ๐’…๐’š/๐’…๐’™ = ใ€–๐Ÿ ๐’†ใ€—^(ใ€–๐’”๐’†๐’„ใ€—^๐Ÿโก๐’™ ). ใ€–๐’”๐’†๐’„ใ€—^๐Ÿ ๐’™ .๐’•๐’‚๐’โก๐’™ โˆ’ ๐Ÿ‘/โˆš(๐Ÿ โˆ’ ๐’™^๐Ÿ )

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.