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Transcript

Ex 12.2, 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.