Examples 30 i.jpg

Examples 30 ii.jpg

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

Transcript

Example 30 Differentiate โˆš(((๐‘ฅโˆ’3) (๐‘ฅ2+4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5)) ๐‘ค.๐‘Ÿ.๐‘ก. ๐‘ฅ. Let y =โˆš(((๐‘ฅโˆ’ 3) (๐‘ฅ2+ 4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5)) Taking log on both sides logโก๐‘ฆ = log โˆš(((๐‘ฅ โˆ’ 3) (๐‘ฅ2 + 4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5)) logโก๐‘ฆ = logโก (((๐‘ฅ โˆ’ 3) (๐‘ฅ2 + 4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5))^(1/2) logโก๐‘ฆ = 1/2 log ((๐‘ฅโˆ’ 3 ) (๐‘ฅ2 + 4))/((3๐‘ฅ2+ 4๐‘ฅ + 5) ) ๐‘ˆ๐‘ ๐‘–๐‘›๐‘” ๐‘™๐‘œ๐‘”โก๐‘Ž๐‘=๐‘™๐‘œ๐‘”โก๐‘Ž+๐‘๐‘œ๐‘ โก๐‘ ๐‘Ž๐‘›๐‘‘ ๐‘™๐‘œ๐‘”โกใ€–๐‘Ž/๐‘ใ€—=๐‘™๐‘œ๐‘”โกใ€–๐‘Žโˆ’๐‘™๐‘œ๐‘”โก๐‘ ใ€— logโก๐‘ฆ = 1/2 (logโกใ€– (๐‘ฅโˆ’3)ใ€—+ใ€–log ใ€—โก(๐‘ฅ2 + 4)โˆ’logโกใ€– (3๐‘ฅ2 + 4๐‘ฅ + 5)ใ€— ) Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ (๐‘‘ (logโก๐‘ฆ))/๐‘‘๐‘ฅ = 1/2 ((๐‘‘(logโก(๐‘ฅโˆ’3)+ใ€–log ใ€—โกใ€–(๐‘ฅ^2+4)โˆ’logโกใ€– (3๐‘ฅ^2+4๐‘ฅ+5)ใ€— ใ€— ) )/๐‘‘๐‘ฅ) (๐‘‘ (logโก๐‘ฆ))/๐‘‘๐‘ฅ = 1/2 ((๐‘‘ logโก(๐‘ฅโˆ’3) )/๐‘‘๐‘ฅ " + " (๐‘‘ logโก(๐‘ฅ^2+4))/๐‘‘๐‘ฅ " โˆ’ " (๐‘‘ logโกใ€– (3๐‘ฅ^2+4๐‘ฅ+5)ใ€—)/๐‘‘๐‘ฅ) 1/๐‘ฆ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = 1/2 ร— 1/(๐‘ฅ โˆ’ 3) . ๐‘‘(๐‘ฅ โˆ’3)/๐‘‘๐‘ฅ + 1/(๐‘ฅ^2 + 4) . (๐‘‘ (๐‘ฅ^2 + 4))/๐‘‘๐‘ฅ โ€“ 1/((3๐‘ฅ^2+ 4๐‘ฅ+ 5)) . (๐‘‘ (3๐‘ฅ^2+ 4๐‘ฅ+ 5))/(๐‘‘๐‘ฅ ) 1/๐‘ฆ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = 1/2 [1/((๐‘ฅ โˆ’ 3) ) " " (1โˆ’0) "+ " 1/(๐‘ฅ^2+ 4) " " (2๐‘ฅ + 0)" โˆ’ " 1/(3๐‘ฅ^2+ 4๐‘ฅ+ 5) " " (6๐‘ฅ +4+0)" " ] 1/๐‘ฆ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = 1/2 (1/((๐‘ฅ โˆ’ 3) )+2๐‘ฅ/(๐‘ฅ^2+ 4)โˆ’(6๐‘ฅ + 4)/(3๐‘ฅ^2+ 4๐‘ฅ+ 5)) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘ฆ/2 (1/((๐‘ฅ โˆ’ 3) )+2๐‘ฅ/(๐‘ฅ^2+ 4)โˆ’(6๐‘ฅ + 4)/(3๐‘ฅ^2+ 4๐‘ฅ+ 5)) ๐’…๐’š/๐’…๐’™ = ๐Ÿ/๐Ÿ โˆš(((๐’™ โˆ’ ๐Ÿ‘)(๐’™^๐Ÿ+ ๐Ÿ’))/(๐Ÿ‘๐’™^๐Ÿ+ ๐Ÿ’๐’™ + ๐Ÿ“)) (๐Ÿ/((๐’™ โˆ’ ๐Ÿ‘) )+๐Ÿ๐’™/(๐’™^๐Ÿ+ ๐Ÿ’)โˆ’(๐Ÿ”๐’™ + ๐Ÿ’)/(๐Ÿ‘๐’™^๐Ÿ+ ๐Ÿ’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.