Example 30 - Differentiate root (x-3)(x2+4)/3x2+4x+5 - Examples

Slide21.JPG

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

Transcript

Example 30 Differentiate ﷮ 𝑥−3﷯ (𝑥2+4)﷮ 3𝑥2+ 4𝑥 + 5﷯﷯ 𝑤.𝑟.𝑡. 𝑥. Let y = ﷮ 𝑥− 3﷯ (𝑥2+ 4)﷮ 3𝑥2+ 4𝑥 + 5﷯﷯ Taking log on both sides log⁡𝑦 = log ﷮ 𝑥 − 3﷯ (𝑥2 + 4)﷮ 3𝑥2+ 4𝑥 + 5﷯﷯ log﷮𝑦﷯ = log⁡ 𝑥 − 3﷯ (𝑥2 + 4)﷮ 3𝑥2+ 4𝑥 + 5﷯﷯﷮ 1﷮2﷯﷯ log﷮𝑦﷯ = 1﷮2﷯ log 𝑥− 3 ﷯ (𝑥2 + 4)﷮ 3𝑥2+ 4𝑥 + 5﷯﷯ log﷮𝑦﷯ = 1﷮2﷯ log﷮ 𝑥−3﷯﷯+ log ﷮ 𝑥2 + 4﷯﷯− log﷮ 3𝑥2 + 4𝑥 + 5﷯﷯﷯ Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑 ( log﷮𝑦﷯)﷮𝑑𝑥﷯ = 1﷮2﷯ 𝑑 log﷮ 𝑥−3﷯﷯+ log ﷮ 𝑥﷮2﷯+4﷯− log﷮ 3 𝑥﷮2﷯+4𝑥+5﷯﷯﷯﷯ ﷮𝑑𝑥﷯﷯ 𝑑 ( log﷮𝑦﷯)﷮𝑑𝑥﷯ = 1﷮2﷯ 𝑑 log﷮ 𝑥−3﷯﷯ ﷮𝑑𝑥﷯ + 𝑑 log﷮ 𝑥﷮2﷯+4﷯﷯﷮𝑑𝑥﷯ − 𝑑 log﷮ 3 𝑥﷮2﷯+4𝑥+5﷯﷯﷮𝑑𝑥﷯﷯ 1﷮𝑦﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯ = 1﷮2﷯ × 1﷮𝑥 − 3﷯ . 𝑑 𝑥 −3﷯﷮𝑑𝑥﷯ + 1﷮ 𝑥﷮2﷯ + 4﷯ . 𝑑 ( 𝑥﷮2﷯ + 4)﷮𝑑𝑥﷯ – 1﷮(3 𝑥﷮2﷯+ 4𝑥+ 5)﷯ . 𝑑 (3 𝑥﷮2﷯+ 4𝑥+ 5)﷮𝑑𝑥 ﷯ 1﷮𝑦﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯ == 1﷮2﷯ 1﷮ 𝑥 − 3﷯﷯ (1−0) + 1﷮ 𝑥﷮2﷯+ 4﷯ (2𝑥 + 0) − 1﷮3 𝑥﷮2﷯+ 4𝑥+ 5﷯ (6𝑥 +4+0) ﷯ 1﷮𝑦﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯ = 1﷮2﷯ 1﷮ 𝑥 − 3﷯﷯+ 2﷮ 𝑥﷮2﷯+ 4﷯− 6𝑥 + 4﷮3 𝑥﷮2﷯+ 4𝑥+ 5﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑦﷮2﷯ 1﷮ 𝑥 − 3﷯﷯+ 2﷮ 𝑥﷮2﷯+ 4﷯− 6𝑥 + 4﷮3 𝑥﷮2﷯+ 4𝑥+ 5﷯﷯ 𝒅𝒚﷮𝒅𝒙﷯ = ﷮ 𝒙 − 𝟑﷯( 𝒙﷮𝟐﷯+ 𝟒)﷮𝟑 𝒙﷮𝟐﷯+ 𝟒𝒙 + 𝟓﷯﷯ 𝟏﷮ 𝒙 − 𝟑﷯﷯+ 𝟐﷮ 𝒙﷮𝟐﷯+ 𝟒﷯− 𝟔𝒙 + 𝟒﷮𝟑 𝒙﷮𝟐﷯+ 𝟒𝒙+ 𝟓﷯﷯

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 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail