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Ex 13.2, 7 - For constants a, b, find derivative of - Derivatives by formula - x^n formula

Ex 13.2, 7 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Ex 13.2, 7 - Chapter 13 Class 11 Limits and Derivatives - Part 3

 


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Ex 13.2, 7 (Method 1) For some constants a and b, find the derivative of (i) (x – a) (x – b) Let f (x) = (x – a) (x – b) = x (x – b) – a (x – b) = x2 – xb – ax + ab = x2 – (b + a)x + ab f’(x) = (x2 – (b + a)x + ab)’ = 2.x2–1 – (b + a) .1x1–1 + 0 = 2x1 – (b + a) . x0 = 2x – (b + a) × 1 = 2x – (b + a) Ex 13.2, 7 (Method 2) For some constants a and b, find the derivative of (i) (x – a) (x – b) Let f (x) = (x – a) (x – b) Let u = (x – a) & v = (x – b) ∴ f(x) = uv So, f’(x) = (uv)’ f’(x) = u’v + v’u Finding u’ & v’ u = x – a u’ = 1. x1–1 – 0 = 1. x0 = 1 v = (x – b) v’ = 1 .x1–1 – 0 = 1 . x0 = 1 Now, f’ (x) = (uv)’ = u’ v + v’u = (1) (x – b) + 1(x – a) = x – b + (x – a) = 2x – b – a = 2x – (b + a)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.