# Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5x+72x-13. - Mathematics and Statistics

Sum

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = (5"x" + 7)/("2x" - 13).

#### Solution

y = (5"x" + 7)/("2x" - 13)

Differentiating both sides w.r.t. x, we get

"dy"/"dx" = "d"/"dx" ((5"x" + 7)/("2x" - 13))

= (("2x" - 13) "d"/"dx" ("5x" + 7) - ("5x" + 7)"d"/"dx"("2x" - 13))/(2"x" - 13)^2

= (("2x" - 13)(5 xx 1 + 0) - ("5x" + 7)(2xx 1 - 0))/(2"x" - 13)^2

= ((2"x" - 13)(5) - ("5x" + 7)(2))/(2"x" - 13)^2

= (10"x" - 65 - 10"x" - 14)/(2"x" - 13)^2

∴ "dy"/"dx" = (-79)/(2"x" - 13)^2

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/((- 79)/(2"x" - 13)^2)

= (-(2"x" - 13)^2)/79

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 4.05 | Page 100