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Example 10 - Chapter 12 Class 11 Limits and Derivatives
Last updated at August 11, 2026 by Teachoo
Derivatives by 1st principle - At a general point
Chapter 12 Class 11 Limits and Derivatives
Concept wise
- Limits - Definition
- Limits - 0/0 form
- Limits - x^n formula
- Limits - Of Trignometric functions
- Limits - Limit exists
- Derivatives by 1st principle - At a point
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Derivatives by 1st principle - At a general point
- Derivatives by formula - x^n formula
- Derivatives by formula - sin & cos
- Derivatives by formula - other trignometric
Transcript
Example 10 Find the derivative of f(x) = x2. Given f(x) = x2 We need to find derivative of f(x) i.e. f’ (x) We know that f’(x) = limh→0 f x + h − f(x)h Here, f (x) = x2 So, f (x + h) = (x + h)2 Putting values f’ (x) = limh→0 𝑥 + ℎ2 − 𝑥2ℎ = limh→0 𝑥2 + ℎ2 + 2𝑥ℎ − 𝑥2 ℎ = limh→0 ℎ2 + 2𝑥ℎ − 𝑥2 + 𝑥2ℎ = limh→0 ℎ ℎ + 2𝑥 + 0ℎ = limh→0 ℎ (ℎ + 2𝑥)ℎ = limh→0 h + 2x Putting h = 0 = 0 + 2x = 2x Hence f’(x) = 2x
