Slide6.JPG

Slide7.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Concept wise

Transcript

Find the derivative of f given by f (x) = cos–1 π‘₯ assuming it exists. Let y = cos–1 π‘₯ cos⁑𝑦= π‘₯ π‘₯ =cos⁑𝑦 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ (𝑑(π‘₯))/𝑑π‘₯ = (𝑑 (cos⁑𝑦 ))/𝑑π‘₯ 1 = (𝑑 (cos⁑𝑦 ))/𝑑π‘₯ We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (cos⁑𝑦 ))/𝑑π‘₯ Γ— 𝑑𝑦/𝑑𝑦 1 = βˆ’sin⁑𝑦 . 𝑑𝑦/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/(βˆ’ π’”π’Šπ’β‘π’š) 𝑑𝑦/𝑑π‘₯ = (βˆ’1)/(√(𝟏 βˆ’ 〖𝒄𝒐𝒔〗^πŸβ‘π’š ) " " ) We know that sin2 𝑦 + cos2 𝑦 = 1 sin2 𝑦 = 1 βˆ’ cos2 𝑦 sin 𝑦 = √(1βˆ’cos^2⁑𝑦 ) Putting value of π‘π‘œπ‘ β‘π‘¦ = π‘₯ 𝑑𝑦/𝑑π‘₯ = (βˆ’1)/(√(1 βˆ’ 𝒙^𝟐 ) " " ) As 𝑦 = cos^(βˆ’1) π‘₯ So, π‘π‘œπ‘ β‘π‘¦ = π‘₯ Hence, (𝒅(〖𝒄𝒐𝒔〗^(βˆ’πŸ)⁑〖𝒙)γ€—)/𝒅𝒙 = (βˆ’1)/(√(1 βˆ’ 𝒙^𝟐 ) " " )

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.