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

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


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 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.