Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
If y = 10x + 1, then `("d"y)/("d"x)` = 10x.log10
पर्याय
True
False
उत्तर
True
APPEARS IN
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 inverse function of the following : y = x ·7x
Find the derivative of the inverse function of the following : y = x2 + log x
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x5 + 2x3 + 3x, at x = 1
If f(x) = x3 + x – 2, find (f–1)'(0).
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 + 25x2