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

Slide14.JPG

Slide15.JPG
Slide16.JPG Slide17.JPG

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

Transcript

Ex 5.5, 5 Differentiate the functions in, (๐‘ฅ + 3)^2 . (๐‘ฅ + 4)^3 . (๐‘ฅ + 5)^4 Let ๐‘ฆ= (๐‘ฅ + 3)^2 . (๐‘ฅ + 4)^3 . (๐‘ฅ + 5)^4 Taking log both sides logโก๐‘ฆ = log ((๐‘ฅ + 3)^2 . (๐‘ฅ + 4)^3 . (๐‘ฅ + 5)^4 ) logโก๐‘ฆ = log (๐‘ฅ + 3)^2 + log (๐‘ฅ + 4)^3 + log (๐‘ฅ + 5)^4 logโก๐‘ฆ = 2 log (๐‘ฅ + 3) + 3 log (๐‘ฅ + 4) + 4 log (๐‘ฅ + 5) Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ. ๐‘‘(logโก๐‘ฆ )/๐‘‘๐‘ฅ = (๐‘‘ (2 log (๐‘ฅ + 3)" + " 3 log (๐‘ฅ + 4)" + " 4 log (๐‘ฅ + 5)))/๐‘‘๐‘ฅ ๐‘‘(logโก๐‘ฆ )/๐‘‘๐‘ฅ (๐‘‘๐‘ฆ/๐‘‘๐‘ฆ) = ๐‘‘(2 log (๐‘ฅ + 3))/๐‘‘๐‘ฅ + (๐‘‘ (3 log (๐‘ฅ + 4)))/๐‘‘๐‘ฅ + ๐‘‘(4 log (๐‘ฅ + 5))/๐‘‘๐‘ฅ ๐‘‘(logโก๐‘ฆ )/๐‘‘๐‘ฆ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = 2 ๐‘‘(log (๐‘ฅ + 3))/๐‘‘๐‘ฅ + 3 (๐‘‘ (log (๐‘ฅ + 4)))/๐‘‘๐‘ฅ + 4 ๐‘‘(log (๐‘ฅ + 5))/๐‘‘๐‘ฅ 1/๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2. 1/((๐‘ฅ + 3) ) . ๐‘‘(๐‘ฅ + 3)/๐‘‘๐‘ฅ + 3. 1/((๐‘ฅ + 4) ) . ๐‘‘(๐‘ฅ + 4)/๐‘‘๐‘ฅ + 4. 1/((๐‘ฅ + 5) ) . ๐‘‘(๐‘ฅ + 5)/๐‘‘๐‘ฅ 1/๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2/(๐‘ฅ + 3) (๐‘‘๐‘ฅ/๐‘‘๐‘ฅ+๐‘‘(3)/๐‘‘๐‘ฅ) + 3/(๐‘ฅ + 4) (๐‘‘๐‘ฅ/๐‘‘๐‘ฅ+๐‘‘(4)/๐‘‘๐‘ฅ) + 4/(๐‘ฅ +5) (๐‘‘๐‘ฅ/๐‘‘๐‘ฅ+๐‘‘(5)/๐‘‘๐‘ฅ) 1/๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2/(๐‘ฅ + 3) (1+0) + 3/(๐‘ฅ + 4) (1+0) + 4/(๐‘ฅ + 5) (1+0) 1/๐‘ฆ ร— ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2/(๐‘ฅ + 3) + 3/(๐‘ฅ + 4) + 4/(๐‘ฅ + 5) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘ฆ (2/(๐‘ฅ + 3) " + " 3/(๐‘ฅ + 4) " + " 4/(๐‘ฅ + 5)) Putting value of ๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘ฅ + 3)^2 . (๐‘ฅ + 4)^3 . (๐‘ฅ + 5)^(4 ) (2/((๐‘ฅ + 3) ) "+ " 3/((๐‘ฅ + 4) ) " + " 4/((๐‘ฅ + 5) )) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘ฅ + 3)^2 (๐‘ฅ + 4)^3 (๐‘ฅ + 5)^(4 ) ((2(๐‘ฅ + 4) (๐‘ฅ + 5) + 3(๐‘ฅ + 3) (๐‘ฅ + 5) + 4(๐‘ฅ + 3) (๐‘ฅ + 4))/((๐‘ฅ + 3) (๐‘ฅ + 4) (๐‘ฅ + 5) )) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ((๐‘ฅ + 3)^2 (๐‘ฅ + 4)^3 ใ€– (๐‘ฅ + 5)ใ€—^(4 ))/((๐‘ฅ + 3) (๐‘ฅ + 4) (๐‘ฅ + 5) ) (2(๐‘ฅ^2+4๐‘ฅ+5๐‘ฅ+20)+3(๐‘ฅ^2+3๐‘ฅ+5๐‘ฅ+15)+ 4(๐‘ฅ^2+3๐‘ฅ+4๐‘ฅ+12)) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ =(๐‘ฅ + 3) (๐‘ฅ + 4)^2 ใ€– (๐‘ฅ + 5)ใ€—^(3 ) (2(๐‘ฅ^2+9๐‘ฅ+20)+3(๐‘ฅ^2+8๐‘ฅ+15)+4(๐‘ฅ^2+7๐‘ฅ+12)) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ =(๐‘ฅ + 3) (๐‘ฅ + 4)^2 ใ€– (๐‘ฅ + 5)ใ€—^(3 ) (2๐‘ฅ^2+18๐‘ฅ+40+3๐‘ฅ^2+24๐‘ฅ+45+4๐‘ฅ^2+28๐‘ฅ+48) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ =(๐‘ฅ + 3) (๐‘ฅ + 4)^2 ใ€– (๐‘ฅ + 5)ใ€—^(3 ) (2๐‘ฅ^2+3๐‘ฅ^2+4๐‘ฅ^2 18๐‘ฅ+24๐‘ฅ+28๐‘ฅ+40+45+48) ๐’…๐’š/๐’…๐’™ =(๐’™ + ๐Ÿ‘) (๐’™ + ๐Ÿ’)^๐Ÿ ใ€– (๐’™ + ๐Ÿ“)ใ€—^(๐Ÿ‘ ) (๐Ÿ—๐’™^๐Ÿ+๐Ÿ•๐ŸŽ๐’™+๐Ÿ๐Ÿ‘๐Ÿ‘)

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.