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Last updated at April 16, 2024 by Teachoo

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 = ๐ฅ๐จ๐ โกใ(๐ฅ๐จ๐ โกใ๐)ใ ใ/๐ฅ๐จ๐ โก๐ Now, differentiating ๐๐ฆ/๐๐ฅ= ๐(((logโกใ(logโกใ7)ใ ใ)/(log 7))/๐๐ฅ ๐๐ฆ/๐๐ฅ= ๐/๐ฅ๐จ๐ โก๐ (๐(logโกใ(logโก๐ฅ ใ )) )/๐๐ฅ ๐๐ฆ/๐๐ฅ= 1/logโก7 . 1/logโก๐ฅ (๐(logโก๐ฅ))/๐๐ฅ ๐๐ฆ/๐๐ฅ= 1/logโก7 . 1/logโก๐ฅ . 1/๐ฅ ๐ ๐/๐ ๐= ๐/ใ๐ฑ ๐๐๐ใโกใ๐ ๐ฅ๐จ๐ โก๐ ใ (As log 7 is constant) ("As (log x)โฒ =" 1/๐ฅ) ("As (log x)โฒ =" 1/๐ฅ)