Advertisements
Advertisements
प्रश्न
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`
उत्तर
y = `(5x + 7)/(2x - 13)`
Differentiating both sides w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x) ((5x + 7)/(2x - 13))`
= `((2x - 13)*"d"/("d"x) (5x + 7) - (5x + 7)*"d"/("d"x)(2x - 13))/(2x - 13)^2`
= `((2x - 13)(5 xx 1 + 0) - (5x + 7)(2 xx 1 - 0))/(2x - 13)^2`
= `((2x - 13)(5) - (5x + 7)(2))/(2x - 13)^2`
= `(10x - 65 - 10x - 14)/(2x - 13)^2`
∴ `("d"y)/("d"x) = (-79)/(2x - 13)^2`
Now, by derivative of inverse function, the rate of change of demand (x) w.r.t. price(y) is
`("d"x)/("d"y) = 1/((("d"y)/("d"x)))`, where `"dy"/"dx" ne 0`
i.e. `("d"x)/("d"y) = 1/((- 79)/(2x - 13)^2)`
`= (-(2x - 13)^2)/79`
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"` if `xsqrt(x) + ysqrt(y) = asqrt(a)`
Find the second order derivatives of the following : e2x . tan x
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"y)/("d"x)` = ex
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
Differentiate the function from over no 15 to 20 sin (x2 + 5)
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+4)`
The differential equation of (x - a)2 + y2 = a2 is ______
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `(dy) / (dx)` if, `y = e ^ (5x^2 - 2x + 4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
