Check sibling questions

Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 3

Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 4
Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 5

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


Transcript

Ex 12.2, 11 Find the derivative of the following functions: (ii) sec x Let f (x) = sec x f(x) = 1/cos⁡𝑥 Let u = 1 & v = cos x So, f(x) = 𝑢/𝑣 ∴ f’(x) = (𝑢/𝑣)^′ Using quotient rule f’(x) = (𝑢^′ 𝑣 − 𝑣^′ 𝑢)/𝑣^2 Finding u’ & v’ u = 1 u’ = 0 & v = cos x v’ = – sin x Now, f’(x) = (𝑢^′ 𝑣 − 𝑣^′ 𝑢)/𝑣^2 = (0(cos⁡〖𝑥) − (−sin⁡〖𝑥) (1)〗 〗)/(〖𝑐𝑜𝑠〗^2 𝑥) (Derivative of constant is 0) (Derivative of cos x = – sin x) = (0 +〖 sin〗⁡𝑥)/(〖𝑐𝑜𝑠〗^2 𝑥) = 〖 sin〗⁡𝑥/(〖𝑐𝑜𝑠〗^2 𝑥) = 〖 sin〗⁡𝑥/cos⁡𝑥 . 1/cos⁡𝑥 = tan x . sec x Hence f’(x) = tan x . sec x Using tan θ = sin⁡𝜃/𝑐𝑜𝑠𝜃 & 1/cos⁡𝜃 = sec θ

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.