Finding derivative of Exponential & logarithm functions

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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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¦^β² = (π’/π£)^β² ππ¦/ππ₯ = (π’^β² π£ β γπ£ γ^β² π’)/π£^2 ππ¦/ππ₯ = ((cosβ‘π₯ )^β² logβ‘π₯ β (logβ‘π₯ )^β² . γ cosγβ‘π₯)/(logβ‘π₯ )^2 ππ¦/ππ₯ = (βsinβ‘π₯ . logβ‘π₯ β (1 )/π₯ . γ cosγβ‘π₯)/(logβ‘π₯ )^2 ππ¦/ππ₯ = (β(sinβ‘π₯ . logβ‘π₯ + (1 )/π₯ . γ cosγβ‘π₯ ))/(logβ‘π₯ )^2 ππ¦/ππ₯ = β (((π₯ sinβ‘γπ₯ logβ‘γπ₯ + cosβ‘π₯ γ γ)/π₯)/(logβ‘π₯ )^2 ) ππ/ππ = β ((π πππβ‘γπ πππβ‘γπ +γ πππγβ‘π γ γ)/(π (πππβ‘π )^π ))