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 + 50x)`