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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

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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

उत्तर

`1/(1 + 75x^2)` 

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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 = `root(3)(x - 2)`


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y = log(2x – 1)


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Using derivative, prove that: sec–1x + cosec–1x = `pi/(2)`    ...[for |x| ≥ 1]


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`


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

y = `(5"x" + 9)/(2"x" - 10)`


If y = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`


If `"x"^3 + "y"^2 + "xy" = 7` Find `"dy"/"dx"`


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


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


Find `dy/dx`, if y = `sec^-1((1 + x^2)/(1 - x^2))`.


If y = `sin^-1((2tanx)/(1 + tan^2x))`, find `dy/dx`.


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


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