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Question
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x – x2.
Solution
y = 25 + 30x – x2.
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" (25 + 30"x" - "x"^2) = 0 + 30 - 2"x"`
∴ `"dy"/"dx" = 30 - 2"x"`
Now, by the derivative of an 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/(30 - 2"x")`
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