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Choose the correct alternative. If y = log (exx2), then dydx=? - Mathematics and Statistics

MCQ
Sum

Choose the correct alternative.

If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?` 

Options

  • `(2 - "x")/"x"`

  • `("x" - 2)/"x"`

  • `("e - x")/"ex"`

  • `("x - e")/"ex"`

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Solution

`("x" - 2)/"x"`

Explanation:

y = log `("e"^"x"/"x"^2)`

= log (ex) - log (x2)

= x log e - 2 log x

= x(1) - 2 log x

∴ y = x - 2 log x

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

`"dy"/"dx" = 1 - 2(1/"x") = ("x - 2")/"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 1.06 | Page 99
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