Question

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x  – x².

Answer 1

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")`