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Misc 1 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Finding derivative of a function by chain rule
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
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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
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Transcript
Misc 1 Differentiate w.r.t. x the function, (3𝑥2 – 9𝑥 + 5)^9Let 𝑦=(3𝑥2 – 9𝑥 + 5)^9 Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦/𝑑𝑥 = (𝑑(3𝑥2 – 9𝑥 + 5)^9)/𝑑𝑥 = 9(3𝑥2 – 9𝑥 + 5)^(9 −1) . 𝑑(3𝑥2 – 9𝑥 + 5)/𝑑𝑥 = 9(3𝑥2 – 9𝑥 + 5)^8 . (𝑑(3𝑥2)/𝑑𝑥 − 𝑑(9𝑥)/𝑑𝑥 − 𝑑(5)/𝑑𝑥) = 9(3𝑥2 – 9𝑥 + 5)^8 . (6𝑥−9+0) = 9(3𝑥2 – 9𝑥 + 5)^8 . (6𝑥−9) = 9(3𝑥2 – 9𝑥 + 5)^8 . 3(2𝑥−3) = 𝟐𝟕(𝟑𝒙𝟐 – 𝟗𝒙 + 𝟓)^𝟖 (𝟐𝒙−𝟑)
