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

Last updated at Dec. 16, 2024 by Teachoo

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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 = 𝐥𝐨𝐠⁡〖(𝐥𝐨𝐠⁡〖𝒙)〗〗/𝐥𝐨𝐠⁡𝟕 Now, differentiating 𝑑𝑦/𝑑𝑥= 𝑑(((log⁡〖(log⁡〖7)〗〗)/(log 7))/𝑑𝑥 𝑑𝑦/𝑑𝑥= 𝟏/𝐥𝐨𝐠⁡𝟕 (𝑑(log⁡〖(log⁡𝑥 〗 )) )/𝑑𝑥 𝑑𝑦/𝑑𝑥= 1/log⁡7 . 1/log⁡𝑥 (𝑑(log⁡𝑥))/𝑑𝑥 𝑑𝑦/𝑑𝑥= 1/log⁡7 . 1/log⁡𝑥 . 1/𝑥 𝒅𝒚/𝒅𝒙= 𝟏/〖𝐱 𝒍𝒐𝒈〗⁡〖𝟕 𝐥𝐨𝐠⁡𝒙 〗 (As log 7 is constant) ("As (log x)′ =" 1/𝑥) ("As (log x)′ =" 1/𝑥)

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Davneet Singh

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

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