Ex 12.2, 11 (ii) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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
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