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

State whether the following statement is True or False: If y = 10x + 1, then dddydx = 10x.log10 - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

If y = 10x + 1, then `("d"y)/("d"x)` = 10x.log10

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

True

shaalaa.com
Derivatives of Inverse Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.3: Differentiation - Q.3

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


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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 = 12 + 10x + 25x2 


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25x + log(1 + x2)


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


If `"x"^3 + "y"^2 + "xy" = 7` 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)`


Choose the correct alternative:

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


Find 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)`


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


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