Check sibling questions

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

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.