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# Find d2ydx2, if y = x2⋅ex - Mathematics and Statistics

Sum

Find ("d"^2"y")/"dx"^2, if y = "x"^2 * "e"^"x"

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#### Solution

y = "x"^2 * "e"^"x"

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

"dy"/"dx" = "x"^2 * "d"/"dx" ("e"^"x") * "d"/"dx" ("x"^2)

= "x"^2 * "e"^"x" + "e"^"x" ("2x")

"dy"/"dx" = ("x"^2 + 2"x") * "e"^"x"

Again, differentiating both sides w.r.t. x, we get

("d"^2"y")/"dx"^2 = ("x"^2 + 2"x") * "d"/"dx" ("e"^"x") + "e"^"x" * "d"/"dx" ("x"^2 + 2"x")

= ("x"^2 + 2"x") * "e"^"x" + "e"^"x"(2x + 2)

= "e"^"x"("x"^2 + 2"x" + 2"x" + 2)

∴ ("d"^2"y")/"dx"^2 = "e"^"x"("x"^2 + 4"x" + 2)

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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 4.21 | Page 101
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