Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Logarithmic Differentiation - Type 1
Example 29 Important
Ex 5.5, 3 Important
Ex 5.5, 15
Ex 5.5, 5
Ex 5.5, 1 Important
Ex 5.5, 13
Ex 5.5, 14 Important
Ex 5.5, 16 Important
Ex 5.5, 17 Important
Ex 5.5, 18
Example 27 Important
Ex 5.5, 2
Misc 22 Important
Misc 3
Misc 7 Important
Example 41
Misc 9 Important
Example 40 (i)
Logarithmic Differentiation - Type 1
Last updated at June 2, 2023 by Teachoo
Example 28 Differentiate ๐^๐ฅ ๐ค.๐.๐ก.๐ฅ, where a is a positive constant.Let y = ๐^๐ฅ Taking log on both sides logโก๐ฆ = logโก๐^๐ฅ ๐๐๐โก๐ = ๐ ๐๐๐โก ๐ Differentiating both sides ๐ค.๐.๐ก.๐ฅ (๐(logโก๐ฆ))/๐๐ฅ = ๐/๐๐ฅ(๐ฅ logโก๐) (๐(logโก๐ฆ))/๐๐ฅ = logโก๐ (๐๐ฅ/๐๐ฅ) (๐(logโก๐ฆ))/๐๐ฅ = ๐๐๐โก๐ (๐๐๐โกใ๐^๐=๐ ๐๐๐โก๐ ใ) (๐(logโก๐ฆ))/๐๐ฅ . ๐๐ฆ/๐๐ฆ = logโก๐ (๐(logโก๐ฆ))/๐๐ฆ . ๐๐ฆ/๐๐ฅ = logโก๐ 1/๐ฆ . ๐๐ฆ/๐๐ฅ = logโก๐ ๐๐ฆ/๐๐ฅ = ๐ฆ logโก๐ Putting back ๐ฆ = ๐^๐ฅ ๐๐ฆ/๐๐ฅ = ๐^๐ ๐๐๐โก๐