Advertisements
Advertisements
प्रश्न
Find the marginal demand of a commodity where demand is x and price is y.
y = `(5"x" + 9)/(2"x" - 10)`
उत्तर
y = `(5"x" + 9)/(2"x" - 10)`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"((5"x" + 9)/("2x" - 10))`
`= (("2x" - 10)*"d"/"dx"("5x" + 9) - ("5x" + 9) * "d"/"dx"(2"x" - 10))/(2"x" - 10)^2`
`= ((2"x" - 10)(5 + 0) - (5"x" + 9)(2 - 0))/(2"x" - 10)^2`
`= (5(2"x" - 10) - 2(5"x" + 9))/(2"x" - 10)^2`
`= (10"x" - 50 - 10"x" - 18)/(2"x" - 10)^2`
∴ `"dy"/"dx" = (- 68)/(2"x" - 10)^2`
Now, by derivative of inverse function, the marginal demand of a commodity is
`"dx"/"dy" = 1/("dy"/"dx")`, where `"dy"/"dx" ne 0`.
i.e. `"dx"/"dy" = 1/((- 68)/(2"x" - 10)^2) = (- (2"x" - 10)^2)/68`
APPEARS IN
संबंधित प्रश्न
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = e2x-3
Find the derivative of the inverse function of the following : y = x ·7x
Find the derivative of the inverse function of the following : y = x2 + log x
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x5 + 2x3 + 3x, at x = 1
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = ex + 3x + 2
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = 3x2 + 2logx3
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = sin(x – 2) + x2
Using derivative, prove that: sec–1x + cosec–1x = `pi/(2)` ...[for |x| ≥ 1]
If y = f(x) is a differentiable function of x, then show that `(d^2x)/(dy^2) = -(dy/dx)^-3.("d^2y)/(dx^2)`.
If `"x"^3"y"^3 = "x"^2 - "y"^2`, Find `"dy"/"dx"`
Choose the correct alternative:
What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`
The rate of change of demand (x) of a commodity with respect to its price (y), if y = 20 + 15x + x3.
Solution: Let y = 20 + 15x + x3
Diff. w.r.to x, we get
`("d"y)/("d"x) = square + square + square`
∴ `("d"y)/("d"x)` = 15 + 3x2
∴ By derivative of the inverse function,
`("d"x)/("d"y) 1/square, ("d"y)/("d"x) ≠ 0`
∴ Rate of change of demand with respect to price = `1/(square + square)`
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
Find `dy/dx`, if y = `sec^-1((1 + x^2)/(1 - x^2))`.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2
Find the rate of change of demand (x) of a commodity with respect to its price (y) if `y=12+10x+25x^2`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
