Ex 12.2, 11 (ii) - Chapter 12 Class 11 Limits and Derivatives
Last updated at May 7, 2024 by Teachoo
Ex 12.2
Ex 12.2, 1
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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/cosβ‘π₯ Let u = 1 & v = cos x So, f(x) = π’/π£ β΄ fβ(x) = (π’/π£)^β² Using quotient rule fβ(x) = (π’^β² π£ β π£^β² π’)/π£^2 Finding uβ & vβ u = 1 uβ = 0 & v = cos x vβ = β sin x Now, fβ(x) = (π’^β² π£ β π£^β² π’)/π£^2 = (0(cosβ‘γπ₯) β (βsinβ‘γπ₯) (1)γ γ)/(γπππ γ^2 π₯) (Derivative of constant is 0) (Derivative of cos x = β sin x) = (0 +γ sinγβ‘π₯)/(γπππ γ^2 π₯) = γ sinγβ‘π₯/(γπππ γ^2 π₯) = γ sinγβ‘π₯/cosβ‘π₯ . 1/cosβ‘π₯ = tan x . sec x Hence fβ(x) = tan x . sec x Using tan ΞΈ = sinβ‘π/πππ π & 1/cosβ‘π = sec ΞΈ
