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Misc 6 - Find derivative: 1 + 1/x / 1 - 1/x - Chapter 13 CBSE

Misc 6 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Misc 6 - Chapter 13 Class 11 Limits and Derivatives - Part 3


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Misc 6 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (1 + 1/π‘₯)/(1 βˆ’ 1/π‘₯) Let f(x) = (1 + 1/π‘₯)/(1 βˆ’ 1/π‘₯) = ((x + 1)/x)/((x βˆ’ 1)/x) = (x + 1)/x Γ— π‘₯/(π‘₯ βˆ’ 1) = (π‘₯ + 1)/(π‘₯ βˆ’ 1 ) So, f(x) = (π‘₯ + 1)/(π‘₯ βˆ’ 1 ) ∴ f(x) = 𝑒/𝑣 So, f’(x) = (𝑒/𝑣)^β€² = (u^β€² v βˆ’ v^β€² u)/v^2 Now, u = x + 1 u’ = 1 + 0 = 1 v = x – 1 v’ = 1 – 0 = 1 Now, f’(x) = (𝑒/𝑣)^β€² = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = (1 (x βˆ’ 1) βˆ’1 (x + 1) )/(x βˆ’ 1)^2 = (x βˆ’ 1 βˆ’ x βˆ’ 1)/(x βˆ’ 1)^2 = (βˆ’ 2)/(x βˆ’ 1)^2 Hence, f’ (x) = (βˆ’ 𝟐)/(𝐱 βˆ’ 𝟏)^𝟐

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