1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise
3. Examples

Transcript

Example 46 Find f β²(x) if π (π₯) = (sinβ‘π₯ )^(sin π₯)β‘ for all 0 < x < Ο. Let γπ¦=(sinβ‘π₯ )γ^(sin π₯) Taking log on both sides log π¦=log (γsinβ‘π₯γ^sinβ‘π₯ ) log π¦=sinβ‘π₯ . log (sinβ‘π₯ ) Differentiating both sides π€.π.π‘.π₯. π(logβ‘π¦)/ππ₯ = π(sinβ‘π₯ . log (sinβ‘π₯ ))/ππ₯ π(logβ‘π¦ )/ππ₯ (ππ¦/ππ¦) = π(sinβ‘π₯ . log (sinβ‘π₯ ))/ππ₯ π(logβ‘π¦ )/ππ¦ (ππ¦/ππ₯) = π(sinβ‘π₯ . log (sinβ‘π₯ ))/ππ₯ 1/π¦ . ππ¦/ππ₯ = π(sinβ‘π₯ . log (sinβ‘π₯ ))/ππ₯ 1/π¦ ππ¦/ππ₯ = π(sinβ‘π₯ )/ππ₯ . γ log γβ‘(sinβ‘π₯ ) + π(γlog γβ‘(sinβ‘π₯ ) )/ππ₯ . sinβ‘π₯ 1/π¦ ππ¦/ππ₯ = cosβ‘π₯ . γlog γβ‘(sinβ‘π₯ ) + 1/sinβ‘π₯ . π(sinβ‘π₯ )/ππ₯ . sinβ‘π₯ 1/π¦ ππ¦/ππ₯ = γcos γβ‘. γlog γβ‘(sinβ‘π₯ ) + 1/sinβ‘π₯ . cosβ‘π₯.sin π₯ 1/π¦ ππ¦/ππ₯ = cosβ‘π₯.log sin π₯+cosβ‘π₯ ππ¦/ππ₯ = π¦ (cosβ‘π₯.log sin π₯+cosβ‘π₯ ) Putting value of y = (π ππβ‘π₯ )^π ππβ‘π₯ ππ¦/ππ₯ = (sinβ‘π₯ )^sinβ‘π₯ (cosβ‘π₯.log sin π₯+cosβ‘π₯ ) ππ¦/ππ₯ = (sinβ‘π₯ )^sinβ‘π₯ . cosβ‘π₯ (log sin π₯+1) ππ/ππ = γ(π+π₯π¨π  (π¬π’π§ π)) (πππβ‘π )γ^πππβ‘π . πππβ‘π

Examples