Finding derivative of Exponential & logarithm functions

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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Ex 5.4, 1 Differentiate π€.π.π‘. π₯ in , π^π₯/sinβ‘π₯ Let π = π^π₯/sinβ‘π₯ Let π’ =π^π₯ & π£ = sinβ‘π₯ β΄ π = π/π Differentiating both sides π€.π.π‘.π₯ π(π¦)/ππ₯ = π(π’/π£)/ππ₯ ππ¦/ππ₯ = ((π’)^β² π£ β γπ£ γ^β² π’)/π£^2 ππ¦/ππ₯ = ((π’)^β² π£ β γπ£ γ^β² π’)/π£^2 ππ/ππ = (π(π^π )/ππ . πππβ‘π β (π(πππβ‘π ) )/ππ . π^π)/(πππβ‘π )^π ππ¦/ππ₯ = (π^π₯ . sinβ‘π₯ β cosβ‘π₯ . π^π₯)/(sinβ‘π₯ )^2 ππ¦/ππ₯ = (π^π₯ (sinβ‘π₯ β cosβ‘π₯ ))/(sinβ‘π₯ )^2 ππ/ππ = (π^π (πππβ‘π β πππβ‘π ))/γπππγ^πβ‘π