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Ex 5.4, 10 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 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
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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, 10 Differentiate w.r.t. π₯ in, cosβ‘(logβ‘π₯ + π^π₯), π₯ > 0Let π¦ = cosβ‘(logβ‘π₯+ π^π₯ ) Differentiating both sides π€.π.π‘.π₯ π¦^β² = (cosβ‘(logβ‘π₯ + π^π₯ ) )^β² π¦^β²= γβsin γβ‘(logβ‘π₯+π^π₯ ) (logβ‘π₯ + π^π₯ )^β² π¦^β²= γβsin γβ‘(logβ‘π₯+π^π₯ ) ((logβ‘π₯ )^β²+(π^π₯ )^β² ) π¦^β² = γβ sin γβ‘(logβ‘π₯+π^π₯ ) (1/π₯ + π^π₯ ) π^β² = ββ‘(π/π + π^π ) πππ (πππβ‘π + π^π )
