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Misc 2 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 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
-
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
Misc 2 Differentiate π€.π.π‘. π₯ the function sin^3 π₯ + cos^6 π₯ Let π¦=sin^3 π₯ + cos^6 π₯ Differentiating π€.π.π‘.π₯. ππ¦/ππ₯ = π((sin^3 π₯ )" + " (cos^6 π₯" " ))/ππ₯ = π((sin^3 π₯ ))/( ππ₯) + π((cos^6 π₯" " ))/ππ₯ = 3 sin^2 π₯ . π(sinβ‘π₯ )/ππ₯ + 6 cos^5 π₯" ". π(cosβ‘π₯ )/ππ₯ = 3 sin^2 π₯ . cosβ‘π₯ + 6 cos^5 π₯. (βsinβ‘π₯ ) = 3 sin^2 π₯ . cosβ‘π₯ β 6 sinβ‘π₯. cos^5 π₯ = 3 γπππγ^π π . πππβ‘π (πππβ‘πβπ γπππγ^πβ‘π )
