Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative. If x = et+e-t2,y=et-e-t2 then dydx = ? - Mathematics and Statistics

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MCQ
Sum

Choose the correct alternative.

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

Options

  • `"-y"/"x"`

  • `"y"/"x"`

  • `"-x"/"y"`

  • `"x"/"y"`

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Solution

`"x"/"y"`

Explanation:

x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`

∴ `"dx"/"dt" = 1/2 ("e"^"t" - "e"^-"t")` and `"dy"/"dx" = 1/2 ("e"^"t" + "e"^-"t")`

∴ `"dx"/"dt" = "y" and `"dy"/"dt" = "x"` 

∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")) = "x"/"y"`

Concept: Derivatives of Implicit 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 1.09 | Page 99
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