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Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2 - Mathematics and Statistics

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प्रश्न

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2 

बेरीज
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उत्तर

y = 12 + 10x + 25x2 

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

`"dy"/"dx" = "d"/"dx"`(12 + 10x + 25x2)

= 0 + 10 + 25(2x)

= 10 + 50x

Now by derivative of inverse function, the rate of change of demand (x) w.r.t. price (y) is

`"dx"/"dy" = 1/("dy"/"dx")`, where `"dy"/"dx" ne 0`

i.e. `"dx"/"dy" = 1/(10 + 50"x")`

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Derivatives of Inverse Functions
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पाठ 3: Differentiation - EXERCISE 3.2 [पृष्ठ ९२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Differentiation
EXERCISE 3.2 | Q 1. 1) | पृष्ठ ९२

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