Advertisements
Advertisements
प्रश्न
Find the marginal demand of a commodity where demand is x and price is y.
y = `("x + 2")/("x"^2 + 1)`
उत्तर
y = `("x + 2")/("x"^2 + 1)`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"(("x + 2")/("x"^2 + 1))`
`= (("x"^2 + 1) * "d"/"dx"("x + 2") - ("x + 2") * "d"/"dx" ("x"^2 + 1))/("x"^2 + 1)^2`
`= (("x"^2 + 1)(1 + 0) - ("x + 2")("2x" + 0))/("x"^2 + 1)^2`
`= (("x"^2 + 1)(1) - ("x + 2")("2x"))/("x"^2 + 1)^2`
`= ("x"^2 + 1 - 2"x"^2 - 4"x")/("x"^2 + 1)^2`
∴ `"dy"/"dx" = (1 - "4x" - "x"^2)/("x"^2 + 1)^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/((1 - 4"x" - "x"^2)/("x"^2 + 1)^2) = ("x"^2 + 1)^2/(1 - 4"x" - "x"^2)`
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 = 2x + 3
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = `log_2(x/2)`
Find the derivative of the inverse function of the following : y = x cos x
Find the derivative of the inverse function of the following : y = x ·7x
Find the derivative of the inverse function of the following : y = x 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 = sin(x – 2) + x2
If f(x) = x3 + x – 2, find (f–1)'(0).
Using derivative, prove that: tan –1x + cot–1x = `pi/(2)`
State whether the following is True or False:
If f′ is the derivative of f, then the derivative of the inverse of f is the inverse of f′.
If y = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`
If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.
Choose the correct alternative:
What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x3.
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)`
Choose the correct alternative:
If x = at2, y = 2at, then `("d"^2y)/("d"x^2)` = ?
State whether the following statement is True or False:
If y = 7x + 1, then the rate of change of demand (x) of a commodity with respect to its price (y) is 7
Find rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
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.
