Last updated at April 13, 2021 by Teachoo

Transcript

Misc 7 Differentiate w.r.t. x the function, (logโก๐ฅ ) logโก๐ฅ, ๐ฅ>1 Let y = (logโก๐ฅ ) logโก๐ฅ Taking log both sides logโก๐ฆ = log ((logโก๐ฅ ) logโก๐ฅ ) logโก๐ฆ = logโก๐ฅ. ใ logใโกใ (logโก๐ฅ )ใ Differentiating both sides ๐ค.๐.๐ก.๐ฅ. ๐(logโก๐ฆ )/๐๐ฅ = ๐(logโก๐ฅ. ใ logใโกใ (logโก๐ฅ )ใ )/๐๐ฅ (As ๐๐๐โก(๐^๐) = ๐ ๐๐๐โก๐) ๐(logโก๐ฆ )/๐๐ฅ (๐๐ฆ/๐๐ฆ) = ๐(logโก๐ฅ. ใ logใโกใ (logโก๐ฅ )ใ )/๐๐ฅ ๐(logโก๐ฆ )/๐๐ฆ (๐๐ฆ/๐๐ฅ) = ๐(logโก๐ฅ. ใ logใโกใ (logโก๐ฅ )ใ )/๐๐ฅ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = ๐(logโก๐ฅ. ใ logใโกใ (logโก๐ฅ )ใ )/๐๐ฅ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = ๐(logโก๐ฅ )/๐๐ฅ . ใ logใโกใ (logโก๐ฅ )ใ + ๐(ใ logใโกใ (logโก๐ฅ )ใ )/๐๐ฅ .ใ logใโก๐ฅ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = 1/๐ฅ logโกใ (logโก๐ฅ )ใ + 1/logโก๐ฅ . ๐(logโก๐ฅ )/๐๐ฅ . logโก๐ฅ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = 1/๐ฅ logโกใ (logโก๐ฅ )ใ + (๐ (logโก๐ฅ ))/๐๐ฅ Using Product rule As (๐ข๐ฃ)โ = ๐ขโ๐ฃ + ๐ฃโ๐ข where u = log x & v = log (log x) 1/๐ฆ . ๐๐ฆ/๐๐ฅ = 1/๐ฅ logโกใ (logโก๐ฅ )ใ + 1/๐ฅ ๐๐ฆ/๐๐ฅ = ๐ฆ ( 1/๐ฅ + logโกใ (logโก๐ฅ )ใ/๐ฅ) ๐ ๐/๐ ๐ = (๐ฅ๐จ๐ โก๐ )^๐ฅ๐จ๐ โก๐ (๐/๐ + ๐๐๐โกใ (๐๐๐โก๐ )ใ/๐) Hence, ๐๐ฆ/๐๐ฅ = (logโก๐ฅ )^logโก๐ฅ (1/๐ฅ + logโกใ (logโก๐ฅ )ใ/๐ฅ)

Miscellaneous

Misc 1

Misc 2

Misc 3

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7 Important You are here

Misc 8

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18

Misc 19 Important

Misc 20

Misc 21

Misc 22

Misc 23 Important

Chapter 5 Class 12 Continuity and Differentiability (Term 1)

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About the Author

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.