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

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Example 39 (ii) - Differentiate log7 (log x) [with Video] - Teachoo - Examples

part 2 - Example 39 (ii) - Examples - Serial order wise - 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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