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Example 31 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 22, 2023 by Teachoo
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Example 31 You are here
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Transcript
Example 31 Differentiate π^π₯ π€.π.π‘.π₯, where a is a positive constant.Let y = π^π₯ Taking log on both sides logβ‘π¦ = logβ‘π^π₯ πππβ‘π = π πππβ‘ π Differentiating both sides π€.π.π‘.π₯ (π(logβ‘π¦))/ππ₯ = π/ππ₯(π₯ logβ‘π) (π(logβ‘π¦))/ππ₯ = logβ‘π (ππ₯/ππ₯) (π(logβ‘π¦))/ππ₯ = πππβ‘π (πππβ‘γπ^π=π πππβ‘π γ) (π(logβ‘π¦))/ππ₯ . ππ¦/ππ¦ = logβ‘π (π(logβ‘π¦))/ππ¦ . ππ¦/ππ₯ = logβ‘π 1/π¦ . ππ¦/ππ₯ = logβ‘π ππ¦/ππ₯ = π¦ logβ‘π Putting back π¦ = π^π₯ ππ¦/ππ₯ = π^π πππβ‘π
