Maharashtra State BoardHSC Commerce 12th Board Exam
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Find dydx, if x = e3t , y = e4t+5 - Mathematics and Statistics

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Sum

Find `"dy"/"dx"`, if x = e3t , y = `"e"^(4"t" + 5)`

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Solution

x = e3t 

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

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

y = `"e"^(4"t" + 5)`

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

`"dy"/"dt" = "e"^(4"t" + 5) * "d"/"dx" ("4t" + 5) = "e"^(4"t" + 5) * (4 + 0)`

`= 4 * "e"^(4"t" + 5)`

∴ `"dy"/"dx" = (("dy"/"dt"))/(("dy"/"dt")) = (4 * "e"^(4"t" + 5))/(3 "e"^"3t") = 4/3 "e"^("t + 5")`

Concept: Derivatives of Parametric Functions
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