# Ex 13.2, 4 (ii) - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)

Last updated at Aug. 28, 2021 by

Last updated at Aug. 28, 2021 by

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Ex 13.2, 4 Find the derivative of the following functions from first principle. (ii) (x – 1) (x – 2) Let f (x) = (x – 1) (x – 2) = x(x – 2) – 1 (x – 2) = x2 – 2x – x + 2 = x2 – 3x + 2 We need to find Derivative of f(x) i.e. f’ (x) We know that f’(x) = (𝑙𝑖𝑚)┬(ℎ→0) 𝑓〖(𝑥 + ℎ) − 𝑓(𝑥)〗/ℎ Here, f(x) = x2 – 3x + 2 So, f(x + h) = (x + h)2 – 3 (x + h) + 2 Putting values f’(x) = (𝑙𝑖𝑚)┬(ℎ→0)〖([(𝑥 + ℎ)2 − 3(𝑥 + ℎ) + 2] − (𝑥2 − 3 + 2))/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖((𝑥 + ℎ)2 − 3𝑥 − 3ℎ + 2 − 𝑥2 + 3𝑥 − 2)/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖((𝑥 + ℎ)2 −3ℎ − 𝑥2 + 3𝑥 − 3𝑥 + 2 − 2)/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖((𝑥 + ℎ)2 − 𝑥2 −3ℎ )/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖(𝑥2 + ℎ2+ 2𝑥ℎ − 𝑥2 −3ℎ )/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖(ℎ2 + 2𝑥ℎ − 3ℎ − 𝑥2 + 𝑥2)/ℎ〗 = (𝑙𝑖𝑚)┬(ℎ→0)〖(ℎ (ℎ + 2𝑥 − 3) )/ℎ〗 = lim┬(h→0)〖ℎ+2𝑥 −3〗 Putting h = 0 = 0 + 2x – 3 = 2x – 3 Hence f’(x) = 2x – 3

Ex 13.2 (Term 2)

Ex 13.2, 1

Ex 13.2, 2

Ex 13.2, 3

Ex 13.2, 4 (i) Important

Ex 13.2, 4 (ii) You are here

Ex 13.2, 4 (iii) Important

Ex 13.2, 4 (iv)

Ex 13.2, 5

Ex 13.2, 6

Ex 13.2, 7 (i) Important

Ex 13.2, 7 (ii)

Ex 13.2, 7 (iii) Important

Ex 13.2, 8

Ex 13.2, 9 (i)

Ex 13.2, 9 (ii) Important

Ex 13.2, 9 (iii)

Ex 13.2, 9 (iv) Important

Ex 13.2, 9 (v)

Ex 13.2, 9 (vi)

Ex 13.2, 10 Important

Ex 13.2, 11 (i)

Ex 13.2, 11 (ii) Important

Ex 13.2, 11 (iii) Important

Ex 13.2, 11 (iv)

Ex 13.2, 11 (v) Important

Ex 13.2, 11 (vi)

Ex 13.2, 11 (vii) Important

Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)

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Davneet Singh

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.