Logarithmic Differentiation - Type 1

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

### Transcript

Example 28 Differentiate ๐^๐ฅ ๐ค.๐.๐ก.๐ฅ, where a is a positive constant.Let y = ๐^๐ฅ Taking log on both sides logโก๐ฆ = logโก๐^๐ฅ ๐๐๐โก๐ = ๐ ๐๐๐โก ๐ Differentiating both sides ๐ค.๐.๐ก.๐ฅ (๐(logโก๐ฆ))/๐๐ฅ = ๐/๐๐ฅ(๐ฅ logโก๐) (๐(logโก๐ฆ))/๐๐ฅ = logโก๐ (๐๐ฅ/๐๐ฅ) (๐(logโก๐ฆ))/๐๐ฅ = ๐๐๐โก๐ (๐๐๐โกใ๐^๐=๐ ๐๐๐โก๐ ใ) (๐(logโก๐ฆ))/๐๐ฅ . ๐๐ฆ/๐๐ฆ = logโก๐ (๐(logโก๐ฆ))/๐๐ฆ . ๐๐ฆ/๐๐ฅ = logโก๐ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = logโก๐ ๐๐ฆ/๐๐ฅ = ๐ฆ logโก๐ Putting back ๐ฆ = ๐^๐ฅ ๐๐ฆ/๐๐ฅ = ๐^๐ ๐๐๐โก๐

#### 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.