Example 28 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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