# Example 27 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 16, 2020 by Teachoo

Last updated at Jan. 16, 2020 by Teachoo

Transcript

Example 27 Find the derivative of f given by f (x) = tan–1 𝑥 assuming it exists. f (x) = tan–1 𝑥 Let y = tan–1 𝑥 tan𝑦 = 𝑥 ∴ 𝑥 = tan𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(𝑥))/𝑑𝑥 = (𝑑 (tan𝑦 ))/𝑑𝑥 1 = (𝑑 (tan𝑦 ))/𝑑𝑥 We need d𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (tan𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = 〖𝐬𝐞𝐜〗^𝟐 𝒚 . 𝑑𝑦/𝑑𝑥 1 = (𝟏 + 𝒕𝒂𝒏𝟐𝒚) 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/(1 + 〖𝐭𝐚𝐧〗^𝟐𝒚 ) Putting 𝑡𝑎𝑛𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = 1/(1 + 𝒙^𝟐 ) As 𝑦 = tan^(−1) 𝑥 So, tan𝑦 = 𝑥 Hence (𝒅(〖𝐭𝐚𝐧〗^(−𝟏)〖𝒙)〗)/𝒅𝒙 = 𝟏/(𝟏 + 𝒙^𝟐 )

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17 Important

Example 18

Example 19

Example 20 Important

Example 21

Example 22

Example 23

Example 24

Example 25

Example 26 Important

Example 27 You are here

Example 28

Example 29 Important

Example 30 Important

Example 31

Example 32 Important

Example 33 Important

Example 34

Example 35

Example 36 Important

Example 37 Important

Example 38

Example 39

Example 40

Example 41

Example 42 Important

Example 43

Example 44 Important

Example 45 Important

Example 46

Example 47 Important

Example 48

About the Author

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.