Question

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

Answer 1

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")`