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Choose the correct alternative. If y = elogx, then dydx=? - Mathematics and Statistics

MCQ
Sum

Choose the correct alternative.

If y = `"e"^(log "x")`, then `"dy"/"dx" = ?`

Options

  • `("e"^(log "x"))/"x"`

  • `1/"x"`

  • 0

  • `1/2`

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Solution

`("e"^(log "x"))/"x"`

Explanation:

y = `"e"^(log "x")`

Differentiating both sides w.r.t.x, we get

`"dy"/"dx" = "e"^(log "x") * "d"/"dx"`(log x)

`= "e"^(log "x") * 1/"x"`

`= ("e"^(log "x"))/"x"`

Concept: Derivative - Derivatives of Logarithmic Functions
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 1.03 | Page 99
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