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Ex 5.4, 6 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Finding derivative of Exponential & logarithm functions
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
Transcript
Ex 5.4, 6 Differentiate 𝑤.𝑟.𝑡. 𝑥 in , 𝑒^𝑥+ 𝑒^(𝑥^2 ) + 𝑒^(𝑥^3 )+ 𝑒^(𝑥^4 ) + 𝑒^(𝑥^5 )Let 𝑦 = 𝑒^𝑥+ 𝑒^(𝑥^2 ) +... + 𝑒^(𝑥^5 ) y = 𝑒^𝑥+ 𝑒^(𝑥^2 ) + 𝑒^(𝑥^3 )+ 𝑒^(𝑥^4 ) + 𝑒^(𝑥^5 ) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = 𝑑(𝑒^𝑥 " + " 𝑒^(𝑥^2 ) " + " 𝑒^(𝑥^3 ) " + " 𝑒^(𝑥^4 ) " + " 𝑒^(𝑥^5 ) )/𝑑𝑥 = (𝑑(𝑒^𝑥 ) )/𝑑𝑥 + 𝑑(𝑒^(𝑥^2 ) )/𝑑𝑥 + 𝑑(𝑒^(𝑥^3 ) )/𝑑𝑥 + 𝑑(𝑒^(𝑥^4 ) )/𝑑𝑥 + 𝑑(𝑒^(𝑥^5 ) )/𝑑𝑥 = 𝑒^𝑥 + 𝑒^(𝑥^2 ). 𝑑(𝑥^2 )/𝑑𝑥 + 𝑒^(𝑥^3 ). 𝑑(𝑥^3 )/𝑑𝑥 + 𝑒^(𝑥^4 ). 𝑑(𝑥^4 )/𝑑𝑥 + 𝑒^(𝑥^5 ). 𝑑(𝑥^5 )/𝑑𝑥 = 𝒆^𝒙 + 2x𝒆^(𝒙^𝟐 ) + 𝟑𝒙^𝟐 𝒆^(𝒙^𝟑 ) + 𝟒𝒙^𝟑 𝒆^(𝒙^𝟒 ) + 〖𝟓𝒙〗^(𝟒 ) 𝒆^(𝒙^𝟓 )
