Example 44 (i) - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at Aug. 19, 2021 by Teachoo
Transcript
Example 44 Differentiate w.r.t. x, the following function: (i) โ(3๐ฅ+2) + 1/โ(2๐ฅ^2+ 4) Let y = โ(3๐ฅ+2) + 1/โ(2๐ฅ^2+ 4 ) Differentiating ๐ค.๐.๐ก.๐ฅ ๐๐ฆ/๐๐ฅ = ๐(โ(3๐ฅ + 2) " + " 1/โ(2๐ฅ^2 + 4 ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = ๐(โ(3๐ฅ + 2))/๐๐ฅ + ๐(1/โ(2๐ฅ^2 + 4 ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = ๐(โ(3๐ฅ + 2))/๐๐ฅ + (๐(2๐ฅ^2 + 4)^((โ1)/2))/๐๐ฅ Calculating ๐(โ(3๐ฅ + 2))/๐๐ฅ & (๐(2๐ฅ^2 + 4)^((โ1)/2))/๐๐ฅ separately Calculating ๐(โ(๐๐ฑ + ๐))/๐ ๐ ๐(โ(3๐ฅ + 2))/๐๐ฅ = 1/(2โ(3๐ฅ + 2 )) ร ๐(3๐ฅ + 2)/๐๐ฅ = 1/(2โ(3๐ฅ + 2 )) ร (3+0) = ๐/(๐โ(๐๐ + ๐ )) Calculating (๐ (๐๐^๐ + ๐)^((โ๐)/๐))/๐ ๐ (๐(2๐ฅ^2 + 4)^((โ1)/2))/๐๐ฅ = (โ1)/2 ใ(2๐ฅ^2+4)ใ^((โ1)/( 2) โ1) . ๐(2๐ฅ^2+ 4)/๐๐ฅ = (โ1)/2 (2๐ฅ^2+ 4)^((โ3)/( 2)) . (๐(2๐ฅ^2 )/๐๐ฅ + ๐(4)/๐๐ฅ) = (โ1)/2 (2๐ฅ^2+ 4)^((โ3)/( 2)) . (4๐ฅ+0) = (โ4๐ฅ)/2 (2๐ฅ^2+ 4)^((โ3)/( 2)) = (โ๐๐)/(๐๐^๐+ ๐)^(๐/๐) Hence, ๐๐ฆ/๐๐ฅ = ๐(โ(3๐ฅ+2))/๐๐ฅ + ๐(1/โ(2๐ฅ^2+ 4 ))/๐๐ฅ ๐ ๐/๐ ๐ = ๐/(๐โ(๐๐ + ๐ )) โ ๐๐/(๐๐^๐+ ๐)^(๐/( ๐))
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Example 29 (i)
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Example 29 (iv)
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Example 42 Important Deleted for CBSE Board 2022 Exams
Example 43 Deleted for CBSE Board 2022 Exams
Example 44 (i) You are here
Example 44 (ii) Important
Example 44 (iii) Important
Example 45 (i)
Example 45 (ii) Important
Example 45 (iii) Important
Example 46
Example 47 Important
Example 48
Chapter 5 Class 12 Continuity and Differentiability (Term 1)
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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.