# Example 31 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Example 31 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 logโก๐ฆ = ๐ฅ logโก ๐ Differentiating both sides ๐ค.๐.๐ก.๐ฅ (๐(logโก๐ฆ))/๐๐ฅ = ๐/๐๐ฅ(๐ฅ logโก๐) (๐(logโก๐ฆ))/๐๐ฅ = logโก๐ (๐๐ฅ/๐๐ฅ) (๐(logโก๐ฆ))/๐๐ฅ = logโก๐ (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 ๐ ๐/๐ ๐ = ๐^๐ ๐๐๐โก๐

Logarithmic Differentiation - Type 1

Example 31
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Example 32 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 30 Important

Ex 5.5, 2

Misc 23 Important

Misc 3

Misc 7 Important

Example 46

Misc 9 Important

Example 45 Important

Chapter 5 Class 12 Continuity and Differentiability

Concept wise

- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem

About the Author

Davneet Singh

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.