Maharashtra State BoardHSC Commerce 12th Board Exam
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The rate of change of demand (x) of a commodity with respect to its price (y), if y = 20 + 15x + x3. Solution: Let y = 20 + 15x + x3 Diff. w.r.to x, we get dydx=□+□ +□ ∴ dydx = 15 + 3x2 ∴ By deriva - Mathematics and Statistics

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Sum

The rate of change of demand (x) of a commodity with respect to its price (y), if y = 20 + 15x + x3.

Solution: Let y = 20 + 15x + x3

Diff. w.r.to x, we get

`("d"y)/("d"x) = square + square  + square`

∴ `("d"y)/("d"x)` = 15 + 3x2

∴ By derivative of the inverse function,

`("d"x)/("d"y)  1/square, ("d"y)/("d"x) ≠ 0`

∴ Rate of change of demand with respect to price = `1/(square + square)`

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Solution

Let y = 20 + 15x + x3

Diff. w.r.to x, we get

`("d"y)/("d"x)` = 0 + 15 + 3x2

∴ `("d"y)/("d"x)` = 15 + 3x2

∴ By derivative of the inverse function,

`("d"x)/("d"y)  1/(("d"y)/("d"x)), ("d"y)/("d"x) ≠ 0`

∴ Rate of change of demand with respect to price = `1/(15 + 3x^2)` 

Concept: Derivatives of Inverse Functions
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