Ex 12.2, 7 (iii) - Chapter 12 Class 11 Limits and Derivatives

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Ex 12.2, 7 - Find derivative of (x - a) / (x - b) - Teachoo - Ex 12.2

part 2 - Ex 12.2, 7 (iii) - Ex 12.2 - Serial order wise - Chapter 12 Class 11 Limits and Derivatives
part 3 - Ex 12.2, 7 (iii) - Ex 12.2 - Serial order wise - Chapter 12 Class 11 Limits and Derivatives

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Transcript

Ex13.2, 7 For some constants a and b, find the derivative of (iii) (x − a)﷮(x − b)﷯ Let f(x) = (x − a)﷮(x − b)﷯ Let u = (x – a) & v = (x – b) So, f(x) = 𝑢﷮𝑣﷯ f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ f’(x) = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ Finding u’ & v’ u = x – a u’ = 1. x1–1 – 0 = x0 = 1 v = x – b v’ = 1.x1–1 – b = 1.x0 = 1 f’(x) = 𝑢﷮𝑣﷯﷯﷮′﷯ = 𝑢﷮′﷯𝑣 − 𝑣﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ = 1 x − b﷯ − (1) x − a﷯ ﷮ x − b﷯2﷯ = 1 x − b﷯ − (1) x − a﷯ ﷮ x − b﷯2﷯ = x − b − x + a﷮ x − b﷯2﷯ = − b + a﷮ x − b﷯2﷯ = a − b﷮ x − b﷯2﷯ Hence, f’ (x) = 𝐚 − 𝐛﷮ 𝐱 − 𝐛﷯𝟐﷯

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