Misc 4 - Differentiate sin-1 (x root x) - Chapter 5 NCERT - Finding derivative of Inverse trigonometric functions

Slide8.JPG

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

Transcript

Misc 4 Differentiate 𝑤.𝑟.𝑡. 𝑥 the function, 𝑠𝑖𝑛﷮−1﷯ (𝑥 ﷮𝑥﷯), 0 ≤ 𝑥 ≤ 1 Let 𝑦= 𝑠𝑖𝑛﷮−1﷯ (𝑥 ﷮𝑥﷯) 𝑦= 𝑠𝑖𝑛﷮−1﷯ (𝑥 . 𝑥﷮ 1﷮2﷯﷯) 𝑦= 𝑠𝑖𝑛﷮−1﷯ ( 𝑥﷮1 + 1﷮2﷯﷯) 𝑦= 𝑠𝑖𝑛﷮−1﷯ 𝑥﷮ 3﷮2﷯﷯﷯ Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑 𝑠𝑖𝑛﷮−1﷯ ( 𝑥﷮ 3﷮2﷯﷯)﷯﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 1﷮ ﷮1 − 𝑥﷮ 3﷮2﷯﷯﷯﷮2﷯﷯﷯ × 𝑑 𝑥﷯﷮ 3﷮2﷯﷯﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 1﷮ ﷮1 − 𝑥﷮3﷯﷯﷯ × 3﷮2﷯ 𝑥﷯﷮ 3﷮2﷯ −1﷯ = 1﷮ ﷮1 − 𝑥﷮3﷯﷯﷯ × 3﷮2﷯ 𝑥 ﷮ 3 − 2﷮2﷯ ﷯ = 1﷮ ﷮1 − 𝑥﷮3﷯﷯﷯ × 3﷮2﷯ 𝑥 ﷮ 1﷮2﷯ ﷯ = 1﷮ ﷮1 − 𝑥﷮3﷯﷯﷯ × 3﷮2﷯ ﷮𝑥﷯ = 3﷮2﷯ ﷮ 𝑥﷮1 − 𝑥﷮3﷯﷯﷯ Hence 𝒅𝒚﷮𝒅𝒙﷯ = 𝟑﷮𝟐﷯ ﷮ 𝒙﷮𝟏 − 𝒙﷮𝟑﷯﷯﷯

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