Maharashtra State BoardHSC Commerce 12th Board Exam
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Find dydx if x = e3t, y=et. - Mathematics and Statistics

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Sum

Find `"dy"/"dx"` if x = `"e"^"3t",  "y" = "e"^(sqrt"t")`.

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Solution

x = `"e"^"3t"`

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

`"dx"/"dt" = "e"^"3t" * "d"/"dx" ("3t")`

`= "e"^"3t" * (3)`

∴ `"dx"/"dt" = 3"e"^"3t"`

y = `"e"^(sqrt"t")`

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

`"dy"/"dt" = "e"^(sqrt"t") * "d"/"dx" (sqrt"t")`

`"dy"/"dt" = "e"^(sqrt"t") * 1/(2 sqrt"t")`

∴ `"dy"/"dx" = ("dy"/"dt")/("dx"/"dt") = "e"^(sqrt"t")/((2 sqrt"t")/(3"e"^"3t"))`

∴ `"dy"/"dx" = 1/(6 sqrt"t")  "e"^(sqrt"t" - "3t")`

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 4.16 | Page 100
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