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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.4, 9 Differentiate w.r.t. x in, cos⁑π‘₯/log⁑π‘₯ , x > 2 Let 𝑦 = cos⁑π‘₯/log⁑π‘₯ Let 𝑒 = cos⁑π‘₯ & 𝑣 = log⁑π‘₯ ∴ 𝑦 = 𝑒/𝑣 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑦^β€² = (𝑒/𝑣)^β€² 𝑑𝑦/𝑑π‘₯ = (𝑒^β€² 𝑣 βˆ’ 〖𝑣 γ€—^β€² 𝑒)/𝑣^2 𝑑𝑦/𝑑π‘₯ = ((cos⁑π‘₯ )^β€² log⁑π‘₯ βˆ’ (log⁑π‘₯ )^β€² . γ€– cos〗⁑π‘₯)/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = (βˆ’sin⁑π‘₯ . log⁑π‘₯ βˆ’ (1 )/π‘₯ . γ€– cos〗⁑π‘₯)/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = (βˆ’(sin⁑π‘₯ . log⁑π‘₯ + (1 )/π‘₯ . γ€– cos〗⁑π‘₯ ))/(log⁑π‘₯ )^2 𝑑𝑦/𝑑π‘₯ = βˆ’ (((π‘₯ sin⁑〖π‘₯ log⁑〖π‘₯ + cos⁑π‘₯ γ€— γ€—)/π‘₯)/(log⁑π‘₯ )^2 ) π’…π’š/𝒅𝒙 = βˆ’ ((𝒙 π’”π’Šπ’β‘γ€–π’™ π’π’π’ˆβ‘γ€–π’™ +γ€– 𝒄𝒐𝒔〗⁑𝒙 γ€— γ€—)/(𝒙 (π’π’π’ˆβ‘π’™ )^𝟐 ))

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.