Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

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

Transcript

Ex 5.4, 2 (Method 1) Differentiate ๐‘ค.๐‘Ÿ.๐‘ก. x in , ๐‘’^(sin^(โˆ’1) ๐‘ฅ)Let ๐‘ฆ = ๐‘’^(sin^(โˆ’1) ๐‘ฅ) Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ = ๐‘‘(๐‘’^(sin^(โˆ’1) ๐‘ฅ) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(sin^(โˆ’1) ๐‘ฅ) . ๐‘‘(sin^(โˆ’1) ๐‘ฅ)/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(sin^(โˆ’1) ๐‘ฅ) . (1/โˆš(1 โˆ’ ๐‘ฅ^2 )) ๐’…(๐’š)/๐’…๐’™ = ๐’†^(ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ) ๐’™)/โˆš(๐Ÿโˆ’๐’™^๐Ÿ ) (๐‘‘(๐‘’^๐‘ฅ )/๐‘‘๐‘ฅ " = " ๐‘’^๐‘ฅ " " ) Ex 5.4, 2 (Method 2) Differentiate ๐‘ค.๐‘Ÿ.๐‘ก. x in , ๐‘’^(sin^(โˆ’1) ๐‘ฅ)Let ๐‘ฆ = ๐‘’^(sin^(โˆ’1) ๐‘ฅ) Let sin^(โˆ’1) ๐‘ฅ=๐‘ก ๐‘ฆ = ๐‘’^๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ = ๐‘‘(๐‘’^๐‘ก )/๐‘‘๐‘ฅ We need ๐‘‘๐‘ก in denominator, so multiplying & Dividing by ๐‘‘๐‘ก . ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘‘(๐‘’^๐‘ก )/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ก/๐‘‘๐‘ก ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘‘(๐‘’^๐‘ก )/๐‘‘๐‘ฅ ร— ๐‘‘๐‘ก/๐‘‘๐‘ก ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘‘(๐‘’^๐‘ก )/๐‘‘๐‘ก ร— ๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘’^๐‘ก ร— ๐‘‘๐‘ก/๐‘‘๐‘ฅ Putting value of ๐‘ก ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘’^(sin^(โˆ’1) ๐‘ฅ) ร— ๐‘‘(sin^(โˆ’1) ๐‘ฅ)/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘’^(sin^(โˆ’1) ๐‘ฅ) ร— 1/โˆš(1 โˆ’ ๐‘ฅ^2 ) ๐’…๐’š/๐’…๐’™ = ๐’†^(ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ) ๐’™)/โˆš(๐Ÿ โˆ’ ๐’™^๐Ÿ )

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.