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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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