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Ex 12.2, 11 (ii) - Chapter 12 Class 11 Limits and Derivatives
Last updated at May 29, 2023 by Teachoo
Ex 12.2
Ex 12.2, 1
Ex 12.2, 2
Ex 12.2, 3
Ex 12.2, 4 (i) Important
Ex 12.2, 4 (ii)
Ex 12.2, 4 (iii) Important
Ex 12.2, 4 (iv)
Ex 12.2, 5
Ex 12.2, 6
Ex 12.2, 7 (i) Important
Ex 12.2, 7 (ii)
Ex 12.2, 7 (iii) Important
Ex 12.2, 8
Ex 12.2, 9 (i)
Ex 12.2, 9 (ii) Important
Ex 12.2, 9 (iii)
Ex 12.2, 9 (iv) Important
Ex 12.2, 9 (v)
Ex 12.2, 9 (vi)
Ex 12.2, 10 Important
Ex 12.2, 11 (i)
Ex 12.2, 11 (ii) Important You are here
Ex 12.2, 11 (iii) Important
Ex 12.2, 11 (iv)
Ex 12.2, 11 (v) Important
Ex 12.2, 11 (vi)
Ex 12.2, 11 (vii) Important
Transcript
Ex 12.2, 11 Find the derivative of the following functions: (ii) sec x Let f (x) = sec x f(x) = 1/cos𝑥 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/cos𝑥 . 1/cos𝑥 = tan x . sec x Hence f’(x) = tan x . sec x Using tan θ = sin𝜃/𝑐𝑜𝑠𝜃 & 1/cos𝜃 = sec θ
