Check sibling questions

Example 45 - Differentiate (i) cos-1 (sin x) - Chapter 5

Β 

Β 

This video is only available for Teachoo black users

Β 

Example 45 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

Β 

This video is only available for Teachoo black users

Β 

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 45 (Method 1) Differentiate the following 𝑀.π‘Ÿ.𝑑. π‘₯. (i) cos^(βˆ’1) (sin⁑π‘₯) Let 𝑓(π‘₯) = cos^(βˆ’1) (sin⁑π‘₯) 𝑓(π‘₯) = cos^(βˆ’1) (γ€–cos 〗⁑(πœ‹/2 βˆ’π‘₯) ) 𝒇(𝒙) = 𝝅/𝟐 βˆ’π’™ Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑓’(π‘₯) = (𝑑 (πœ‹/2))/𝑑π‘₯ βˆ’ (𝑑(π‘₯))/𝑑π‘₯ 𝑓’(π‘₯) = 0 βˆ’ 1 𝒇’(𝒙) = βˆ’ 1 (𝐴𝑠 γ€– 𝑠𝑖𝑛 πœƒ 〗⁑〖=γ€–π‘π‘œπ‘  〗⁑〖(πœ‹/2 βˆ’π‘₯)γ€— γ€— ) ("As " (𝑑(π‘₯))/𝑑π‘₯ " = 1 & " πœ‹/2 " is constant" ) Example 45 (Method 2) Differentiate the following 𝑀.π‘Ÿ.𝑑. π‘₯. (i) cos^(βˆ’1) (sin⁑π‘₯) Let 𝑓(π‘₯) = cos^(βˆ’1) (sin⁑π‘₯) Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑓′(π‘₯) = (βˆ’1)/√(1 βˆ’ γ€–(sin⁑π‘₯)γ€—^2 ) Γ— (sin⁑π‘₯ )^β€² 𝑓′(π‘₯) = (βˆ’1)/√(1 βˆ’ sin^2⁑π‘₯ ) Γ—cos⁑π‘₯ 𝑓′(π‘₯) = (βˆ’1)/√(cos^2⁑π‘₯ ) Γ—cos⁑π‘₯ 𝑓′(π‘₯) = (βˆ’1)/cos⁑π‘₯ Γ—cos⁑π‘₯ 𝒇’(𝒙) = βˆ’1

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.