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Question 2 - Finding derivative of a function by chain rule - 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
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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
Transcript
Question 2 Differentiate sin β‘(cos β‘(π₯2)) with respect to π₯ .Let π¦ = " " sin β‘(cos β‘π₯2) We need to find derivative of π¦ π€.π.π‘.π₯ i.e. π¦^β² = (π ππβ‘γ (cosβ‘γπ₯^2 γ )γ ) ππ¦/ππ₯ = π(π ππβ‘γ (cosβ‘γπ₯^2 γ )γ )/ππ₯ = cos (cosβ‘γπ₯^2 γ ) . π(cosβ‘γπ₯^2 γ )/ππ₯ = cos (cosβ‘γπ₯^2 γ ). (βsinβ‘γπ₯^2 γ ) . π(π₯^2 )/ππ₯ = cos (cosβ‘γπ₯^2 γ ). (βsinβ‘γπ₯^2 γ ) . 2π₯ = β 2x sin π^π. cos (cos π^π)
