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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: If x = 2am, y = 2am2, where m be the parameter, then dydx = ? - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

If x = 2am, y = 2am2, where m be the parameter, then `("d"y)/("d"x)` = ? 

पर्याय

  • 2m

  • – 2m

  • – am

  • am

MCQ

उत्तर

2m

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Derivatives of Parametric Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.3: Differentiation - Q.1

संबंधित प्रश्‍न

Find `"dy"/"dx"`, if x = `sqrt(1 + "u"^2), "y" = log (1 + "u"^2)`


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Find `("d"y)/("d"x)`, if x = em, y = `"e"^(sqrt("m"))`

Solution: Given, x = em and y = `"e"^(sqrt("m"))`

Now, y = `"e"^(sqrt("m"))`

Diff.w.r.to m,

`("d"y)/"dm" = "e"^(sqrt("m"))("d"square)/"dm"`

∴ `("d"y)/"dm" = "e"^(sqrt("m"))*1/(2sqrt("m"))`    .....(i)

Now, x = em

Diff.w.r.to m,

`("d"x)/"dm" = square`    .....(ii)

Now, `("d"y)/("d"x) = (("d"y)/("d"m))/square`

∴ `("d"y)/("d"x) = (("e"sqrt("m"))/square)/("e"^"m")`

∴  `("d"y)/("d"x) = ("e"^(sqrt("m")))/(2sqrt("m")*"e"^("m")`


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