हिंदी

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

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

True

shaalaa.com
Derivatives of Inverse Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 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


Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = e2x-3 


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 log x


If f(x) = x3 + x – 2, find (f–1)'(0).


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

y = `("x + 2")/("x"^2 + 1)`


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


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


If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(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 = `(3x + 7)/(2x^2 + 5)`


State whether the following statement is True or False:

If y = x2, then the rate of change of demand (x) of a commodity with respect to its price (y) is `1/(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


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 + 25x^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×