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