Example 28 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at June 2, 2023 by Teachoo

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Example 28 Differentiate 𝑎^𝑥 𝑤.𝑟.𝑡.𝑥, where a is a positive constant.Let y = 𝑎^𝑥 Taking log on both sides log⁡𝑦 = log⁡𝑎^𝑥 𝒍𝒐𝒈⁡𝒚 = 𝒙 𝒍𝒐𝒈⁡ 𝒂 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(log⁡𝑦))/𝑑𝑥 = 𝑑/𝑑𝑥(𝑥 log⁡𝑎) (𝑑(log⁡𝑦))/𝑑𝑥 = log⁡𝑎 (𝑑𝑥/𝑑𝑥) (𝑑(log⁡𝑦))/𝑑𝑥 = 𝒍𝒐𝒈⁡𝒂 (𝑙𝑜𝑔⁡〖𝑎^𝑏=𝑏 𝑙𝑜𝑔⁡𝑎 〗) (𝑑(log⁡𝑦))/𝑑𝑥 . 𝑑𝑦/𝑑𝑦 = log⁡𝑎 (𝑑(log⁡𝑦))/𝑑𝑦 . 𝑑𝑦/𝑑𝑥 = log⁡𝑎 1/𝑦 . 𝑑𝑦/𝑑𝑥 = log⁡𝑎 𝑑𝑦/𝑑𝑥 = 𝑦 log⁡𝑎 Putting back 𝑦 = 𝑎^𝑥 𝑑𝑦/𝑑𝑥 = 𝒂^𝒙 𝒍𝒐𝒈⁡𝒂

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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.

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