Maharashtra State BoardHSC Commerce 12th Board Exam
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Find d2ydx2, if y = e(2x+1) - Mathematics and Statistics

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Sum

Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`

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Solution

y = `"e"^((2x + 1))`

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

`("d"y)/("d"x) = "e"^((2x + 1))*"d"/("d"x)(2x + 1)`

∴ `("d"y)/("d"x) = "e"^((2x + 1))*(2 + 0)`

∴ `("d"y)/("d"x) = 2"e"^((2x + 1))`

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

∴ `("d"^2y)/("d"x^2) = 2*"d"/("d"x)"e"^((2x + 1))`

= `2"e"^((2x + 1))*"d"/("d"x)(2x + 1)`

= `2"e"^((2x + 1))*(2 + 0)`

∴ `("d"^2y)/("d"x^2) = 4"e"^((2x + 1))`

Concept: Derivatives of Composite Functions - Chain Rule
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