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Ex 5.4, 9 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 7, 2026 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
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Transcript
Ex 5.4, 9 Differentiate w.r.t. x in, cosβ‘π₯/logβ‘π₯ , x > 2Let π¦ = cosβ‘π₯/logβ‘π₯ Let π’ = cosβ‘π₯ & π£ = logβ‘π₯ β΄ π¦ = (.π’)/π£ Differentiating both sides π€.π.π‘.π₯ π¦^β² = (π’/π£)^β² ππ¦/ππ₯ = (π’^β² π£ β γπ£ γ^β² π’)/π£^2 ππ¦/ππ₯ = ((cosβ‘π₯ )^β² logβ‘π₯ β (logβ‘π₯ )^β² . γ cosγβ‘π₯)/(logβ‘π₯ )^2 ππ¦/ππ₯ = (βsinβ‘π₯ . logβ‘π₯ β (1 )/π₯ . γ cosγβ‘π₯)/(logβ‘π₯ )^2 ππ¦/ππ₯ = (β(sinβ‘π₯ . logβ‘π₯ + (1 )/π₯ . γ cosγβ‘π₯ ))/(logβ‘π₯ )^2 ππ¦/ππ₯ = β (((π₯ sinβ‘γπ₯ logβ‘γπ₯ + cosβ‘π₯ γ γ)/π₯)/(logβ‘π₯ )^2 ) π π/π π = β ((π πππβ‘γπ πππβ‘γπ +γ πππγβ‘π γ γ)/(π (πππβ‘π )^π ))
