1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
  3. Miscellaneous
Check sibling questions

Misc 4 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Misc 4 Differentiate ๐‘ค.๐‘Ÿ.๐‘ก. ๐‘ฅ the function, ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1) (๐‘ฅ โˆš๐‘ฅ), 0 โ‰ค ๐‘ฅ โ‰ค 1 Let ๐‘ฆ=ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1) (๐‘ฅ โˆš๐‘ฅ) ๐‘ฆ=ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1) (๐‘ฅ . ๐‘ฅ^(1/2)) ๐‘ฆ=ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1) (๐‘ฅ^(1 + 1/2)) ๐’š=ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ) (๐’™^( ๐Ÿ‘/๐Ÿ) ) Differentiating ๐‘ค.๐‘Ÿ.๐‘ก. ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘‘(ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1) (๐‘ฅ^( 3/2)))/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/โˆš(1 โˆ’ (๐‘ฅ^(3/2) )^2 ) ร— (๐‘‘(๐‘ฅ)^(3/2))/๐‘‘๐‘ฅ ("As " ๐‘‘(ใ€–๐‘ ๐‘–๐‘›ใ€—^(โˆ’1)โก๐‘ฅ )/๐‘‘๐‘ฅ=1/โˆš(1 โˆ’ ๐‘ฅ^2 )) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/โˆš(1 โˆ’ ๐‘ฅ^3 ) ร— 3/2 (๐‘ฅ)^(3/2 โˆ’1) = 1/โˆš(1 โˆ’ ๐‘ฅ^3 ) ร— 3/2 ใ€–๐‘ฅ ใ€—^(1/2 ) = 1/โˆš(1 โˆ’ ๐‘ฅ^3 ) ร— 3/2 โˆš๐‘ฅ = ๐Ÿ‘/๐Ÿ โˆš(๐’™/(๐Ÿ โˆ’๐’™^๐Ÿ‘ ))
  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

    3. Miscellaneous

    Case Based Questions (MCQ) →
Case Based Questions (MCQ) →
Chapter 5 Class 12 Continuity and Differentiability
Serial order wise

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo