Example 40 (i) - Chapter 5 Class 12 Continuity and Differentiability (Important Question)

Last updated at June 2, 2023 by Teachoo

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

Book a free demo

Transcript

Example 40 (Method 1) Differentiate the following 𝑤.𝑟.𝑡. 𝑥. (i) cos^(−1) (sin⁡𝑥) Let 𝑓(𝑥) = cos^(−1) (sin⁡𝑥) 𝑓(𝑥) = cos^(−1) (〖cos 〗⁡(𝜋/2 −𝑥) ) 𝒇(𝒙) = 𝝅/𝟐 −𝒙 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑓’(𝑥) = (𝑑 (𝜋/2))/𝑑𝑥 − (𝑑(𝑥))/𝑑𝑥 𝑓’(𝑥) = 0 − 1 𝒇’(𝒙) = − 1(𝐴𝑠 〖 𝑠𝑖𝑛 𝜃 〗⁡〖=〖𝑐𝑜𝑠 〗⁡〖(𝜋/2 −𝑥)〗〗 ) ("As " (𝑑(𝑥))/𝑑𝑥 " = 1 & " 𝜋/2 " is constant" ) Example 40 (Method 2) Differentiate the following 𝑤.𝑟.𝑡. 𝑥. (i) cos^(−1) (sin⁡𝑥) Let 𝑓(𝑥) = cos^(−1) (sin⁡𝑥) Differentiating 𝑤.𝑟.𝑡.𝑥 𝑓′(𝑥) = (−1)/√(1 − 〖(sin⁡𝑥)〗^2 ) × (sin⁡𝑥 )^′ 𝑓′(𝑥) = (−1)/√(1 − sin^2⁡𝑥 ) ×cos⁡𝑥 𝑓′(𝑥) = (−1)/√(cos^2⁡𝑥 ) ×cos⁡𝑥 𝑓′(𝑥) = (−1)/cos⁡𝑥 ×cos⁡𝑥 𝒇’(𝒙) = −1

Next: Example 42 Important → Ask a doubt

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.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular