Advertisements
Advertisements
प्रश्न
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
Advertisements
उत्तर
Demand function, D =`sqrt(75 − 3"P")`
Now, Marginal demand = `("dD")/("dP")`
= `"d"/("dP")(sqrt(75 − 3"P"))`
=`1/(2 sqrt(75- 3"P")) *"d"/("dP") (75 - 3"P")`
=`1/(2 sqrt(75- 3"P"))*(0 - 3 xx1)`
=`(-3)/(2 sqrt(75 - 3"P"))`
When P = 5,
Marginal demand = `(("dD")/("dP")) _("P" = 5)`
=`(-3)/(2 sqrt(75 - 3(5)))`
= `(-3)/(2sqrt60)`
= `(-3)/(4sqrt15)`
∴ Marginal demand =`(-3)/(4sqrt15)` at P = 5.
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.
Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Differentiate the following function .w.r.t.x. : x5
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx if y=(1+x)/(2+x)`
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
