मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternatives: What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x3. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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.

पर्याय

  • `10/(1 + 75x^2)` 

  • `1/(1 + 75x^2)` 

  • 1 + 75x2

  • `(-1)/(1 + 75x^2)` 

MCQ
Advertisements

उत्तर

`1/(1 + 75x^2)` 

shaalaa.com
Derivatives of Inverse Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.3: Differentiation - Q.1

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 = `sqrt(2 - sqrt(x)`


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 = 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 = 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 


If y = f(x) is a differentiable function of x, then show that `(d^2x)/(dy^2) = -(dy/dx)^-3.("d^2y)/(dx^2)`.


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 18x + log(x - 4).


Find the marginal demand of a commodity where demand is x and price is y.

y = `"x"*"e"^-"x" + 7`


If `"x"^3"y"^3 = "x"^2 - "y"^2`, Find `"dy"/"dx"`


If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.


If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______


Find the derivative of the inverse of function y = 2x3 – 6x and calculate its value at x = −2


Let f(x) = x5 + 2x – 3 find (f−1)'(-3)


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 xm. yn = `("x" + "y")^(("m" + "n"))`, then `("dy")/("dx")` = ?


Choose the correct alternative:

If x = at2, y = 2at, then `("d"^2y)/("d"x^2)` = ?


The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = 5 + x2e–x + 2x


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x2e–x + 2x


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)`


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2


I.F. of dx = y (x + y ) dy is a function of ______.


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))`.


If y = `cos^-1 sqrt((1 + x^2)/2`, then `dy/dx` = ______.


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


Find the rate of change of demand (x) of a commodity with respect to its price (y) if `y=12+10x+25x^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×