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

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

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

  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

Ex 13.2, 11 Find the derivative of the following functions: (ii) sec x Let f (x) = sec x f(x) = 1/cos⁑π‘₯ Let u = 1 & v = cos x So, f(x) = 𝑒/𝑣 ∴ f’(x) = (𝑒/𝑣)^β€² Using quotient rule f’(x) = (𝑒^β€² 𝑣 βˆ’ 𝑣^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = 1 u’ = 0 & v = cos x v’ = – sin x Now, f’(x) = (𝑒^β€² 𝑣 βˆ’ 𝑣^β€² 𝑒)/𝑣^2 = (0(cos⁑〖π‘₯) βˆ’ (βˆ’sin⁑〖π‘₯) (1)γ€— γ€—)/(γ€–π‘π‘œπ‘ γ€—^2 π‘₯) (Derivative of constant is 0) (Derivative of cos x = – sin x) = (0 +γ€– sin〗⁑π‘₯)/(γ€–π‘π‘œπ‘ γ€—^2 π‘₯) = γ€– sin〗⁑π‘₯/(γ€–π‘π‘œπ‘ γ€—^2 π‘₯) = γ€– sin〗⁑π‘₯/cos⁑π‘₯ . 1/cos⁑π‘₯ = tan x . sec x Hence f’(x) = tan x . sec x Using tan ΞΈ = sinβ‘πœƒ/π‘π‘œπ‘ πœƒ & 1/cosβ‘πœƒ = sec ΞΈ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.