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Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 7

Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 8

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Example 44 Differentiate w.r.t. x, the following function: (iii) log7 (log x) y = log7 (log x) But we do not solve base 7. So, changing base y = log7 ( log x) y = π₯𝐨𝐠⁑〖(π₯𝐨𝐠⁑〖𝒙)γ€— γ€—/π₯π¨π β‘πŸ• Now, differentiating 𝑑𝑦/𝑑π‘₯= 𝑑(((log⁑〖(log⁑〖7)γ€— γ€—)/(log 7))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯= 𝟏/π₯π¨π β‘πŸ• (𝑑(log⁑〖(log⁑π‘₯ γ€— )) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯= 1/log⁑7 . 1/log⁑π‘₯ (𝑑(log⁑π‘₯))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯= 1/log⁑7 . 1/log⁑π‘₯ . 1/π‘₯ π’…π’š/𝒅𝒙= 𝟏/〖𝐱 π’π’π’ˆγ€—β‘γ€–πŸ• π₯𝐨𝐠⁑𝒙 γ€— (As log 7 is constant) ("As (log x)β€² =" 1/π‘₯) ("As (log x)β€² =" 1/π‘₯)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.