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