Advertisements
Advertisements
Question
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 18x + log(x - 4).
Solution
y = 18x + log(x - 4)
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"`[18x + log(x - 4)]
`= "d"/"dx" (18"x") + "d"/"dx"`[log (x - 4)]
`= 18 + 1/("x - 4") * "d"/"dx"`(x - 4)
`= 18 + 1/("x - 4") * (1 - 0)`
`= 18 + 1/"x - 4"`
`= (18 ("x - 4") + 1)/("x - 4")`
`= (18"x" - 72 + 1)/("x - 4")`
∴ `"dy"/"dx" = (18"x" - 71)/("x - 4")`
Now, by a derivative of inverse function, the rate of change of demand (x) w.r.t. price (y) is
`"dx"/"dy" = 1/("dy"/"dx")`, where `"dy"/"dx" ne 0`.
i.e. `"dx"/"dy" = 1/((18"x" - 71)/("x - 4")) = ("x - 4")/(18"x" - 71)`
APPEARS IN
RELATED QUESTIONS
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)`
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)`
If f(x) = x3 + x – 2, find (f–1)'(0).
Choose the correct option from the given alternatives :
If g is the inverse of function f and f'(x) = `(1)/(1 + x)`, then the value of g'(x) is equal to :
Find the marginal demand of a commodity where demand is x and price is y.
y = `("x + 2")/("x"^2 + 1)`
If y = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`
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)`
The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = 5 + x2e–x + 2x
The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = xe–x + 7
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x2e–x + 2x
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.
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 the rate of change of demand (x) of a commodity with respect to its price (y) if `y=12+10x+25x^2`
