Check sibling questions

  Slide11.JPG

Slide12.JPG
Slide13.JPG

This video is only available for Teachoo black users

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 27 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‘ฅ โˆ’ 3) (๐‘ฅ^2 + 4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5)) Taking log on both sides ๐’๐’๐’ˆโก๐’š = ๐’๐’๐’ˆ โˆš(((๐’™ โˆ’ ๐Ÿ‘) (๐’™๐Ÿ + ๐Ÿ’))/( ๐Ÿ‘๐’™๐Ÿ+ ๐Ÿ’๐’™ + ๐Ÿ“)) logโก๐‘ฆ = logโก (((๐‘ฅ โˆ’ 3) (๐‘ฅ2 + 4))/( 3๐‘ฅ2+ 4๐‘ฅ + 5))^(1/2) ๐’๐’๐’ˆโก๐’š = ๐Ÿ/๐Ÿ log ((๐‘ฅ โˆ’ 3) (๐‘ฅ2 + 4))/((3๐‘ฅ2+ 4๐‘ฅ + 5) ) (๐‘ˆ๐‘ ๐‘–๐‘›๐‘” logโกใ€–๐‘Ž^๐‘ ใ€—=๐‘ logโก๐‘Ž) ๐’๐’๐’ˆโก๐’š = ๐Ÿ/๐Ÿ log ((๐‘ฅ โˆ’ 3) (๐‘ฅ2 + 4))/((3๐‘ฅ2+ 4๐‘ฅ + 5) ) ๐‘™๐‘œ๐‘”โ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ก(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) " . " 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 )] ๐‘ˆ๐‘ ๐‘–๐‘›๐‘” ๐‘™๐‘œ๐‘”โก๐‘Ž๐‘=๐‘™๐‘œ๐‘”โก๐‘Ž+๐‘๐‘œ๐‘ โก๐‘ &๐‘™๐‘œ๐‘”โกใ€–๐‘Ž/๐‘ใ€—=๐‘™๐‘œ๐‘”โกใ€–๐‘Žโˆ’๐‘™๐‘œ๐‘”โก๐‘ ใ€— 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“))

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.