Example 39 (ii) - Chapter 5 Class 12 Continuity and Differentiability

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Example 39 Differentiate w.r.t. x, the following function: (ii) log7 (log x) y = log7 (log x) But we do not solve base 7. So, changing base y = log7 ( log x) y = ๐ฅ๐จ๐ โกใ€–(๐ฅ๐จ๐ โกใ€–๐’™)ใ€— ใ€—/๐ฅ๐จ๐ โก๐Ÿ• Now, differentiating ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐‘‘(((logโกใ€–(logโกใ€–7)ใ€— ใ€—)/(log 7))/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= ๐Ÿ/๐ฅ๐จ๐ โก๐Ÿ• (๐‘‘(logโกใ€–(logโก๐‘ฅ ใ€— )) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= 1/logโก7 . 1/logโก๐‘ฅ (๐‘‘(logโก๐‘ฅ))/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= 1/logโก7 . 1/logโก๐‘ฅ . 1/๐‘ฅ ๐’…๐’š/๐’…๐’™= ๐Ÿ/ใ€–๐ฑ ๐’๐’๐’ˆใ€—โกใ€–๐Ÿ• ๐ฅ๐จ๐ โก๐’™ ใ€— (As log 7 is constant) ("As (log x)โ€ฒ =" 1/๐‘ฅ) ("As (log x)โ€ฒ =" 1/๐‘ฅ)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo