Example 22 - Chapter 13 Class 11 Limits and Derivatives - Part 4

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Example 22 - Chapter 13 Class 11 Limits and Derivatives - Part 5

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  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

Example 22 Find the derivative of (ii) (π‘₯ + π‘π‘œπ‘ β‘π‘₯)/π‘‘π‘Žπ‘›β‘π‘₯ Let f(x) = (π‘₯ + π‘π‘œπ‘ β‘π‘₯)/π‘‘π‘Žπ‘›β‘π‘₯ Let u = x + cos x & v = tan x ∴ f(x) = 𝑒/𝑣 So, f’(x) = (𝑒/𝑣)^β€² Using quotient rule f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = x + cos x u’ = (x + cos x)’ = 1 – sin x v = tan x v’ = sec2x Now, f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = ((𝟏 βˆ’γ€– 𝐬𝐒𝐧〗⁑〖𝒙) (π­πšπ§β‘γ€–π’™) βˆ’ π’”π’†π’„πŸπ’™ (𝒙 + γ€– πœπ¨π¬γ€—β‘γ€–π’™)γ€— γ€— γ€—)/γ€–(π­πšπ§β‘γ€–π’™)γ€—γ€—^𝟐 (xn)’ = n xn – 1 Derivative of cos x = –sin x Derivative of tan x = sec2x (Calculated in Example 17)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.