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

Last updated at March 11, 2021 by Teachoo

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

Transcript

Ex 5.4, 2 (Method 1) Differentiate ๐ค.๐.๐ก. x in , ๐^(sin^(โ1) ๐ฅ)Let ๐ฆ = ๐^(sin^(โ1) ๐ฅ) Differentiating both sides ๐ค.๐.๐ก.๐ฅ ๐(๐ฆ)/๐๐ฅ = ๐(๐^(sin^(โ1) ๐ฅ) )/๐๐ฅ ๐๐ฆ/๐๐ฅ = ๐^(sin^(โ1) ๐ฅ) . ๐(sin^(โ1) ๐ฅ)/๐๐ฅ ๐๐ฆ/๐๐ฅ = ๐^(sin^(โ1) ๐ฅ) . (1/โ(1 โ ๐ฅ^2 )) ๐ (๐)/๐ ๐ = ๐^(ใ๐๐๐ใ^(โ๐) ๐)/โ(๐โ๐^๐ ) (๐(๐^๐ฅ )/๐๐ฅ " = " ๐^๐ฅ " " ) Ex 5.4, 2 (Method 2) Differentiate ๐ค.๐.๐ก. x in , ๐^(sin^(โ1) ๐ฅ)Let ๐ฆ = ๐^(sin^(โ1) ๐ฅ) Let sin^(โ1) ๐ฅ=๐ก ๐ฆ = ๐^๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ ๐(๐ฆ)/๐๐ฅ = ๐(๐^๐ก )/๐๐ฅ We need ๐๐ก in denominator, so multiplying & Dividing by ๐๐ก . ๐๐ฆ/๐๐ฅ= ๐(๐^๐ก )/๐๐ฅ ร ๐๐ก/๐๐ก ๐๐ฆ/๐๐ฅ= ๐(๐^๐ก )/๐๐ฅ ร ๐๐ก/๐๐ก ๐๐ฆ/๐๐ฅ= ๐(๐^๐ก )/๐๐ก ร ๐๐ก/๐๐ฅ ๐๐ฆ/๐๐ฅ= ๐^๐ก ร ๐๐ก/๐๐ฅ Putting value of ๐ก ๐๐ฆ/๐๐ฅ= ๐^(sin^(โ1) ๐ฅ) ร ๐(sin^(โ1) ๐ฅ)/๐๐ฅ ๐๐ฆ/๐๐ฅ= ๐^(sin^(โ1) ๐ฅ) ร 1/โ(1 โ ๐ฅ^2 ) ๐ ๐/๐ ๐ = ๐^(ใ๐๐๐ใ^(โ๐) ๐)/โ(๐ โ ๐^๐ )

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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.