Example 31 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

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Example 31 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

Logarithmic Differentiation - Type 1

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Chapter 5 Class 12 Continuity and Differentiability

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.