Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If xm. yn = `("x" + "y")^(("m" + "n"))`, then `("dy")/("dx")` = ?
पर्याय
`"y"/"x"`
`(-"y")/"x"`
`"x"/"y"`
`(-"x")/"y"`
उत्तर
`"y"/"x"`
APPEARS IN
संबंधित प्रश्न
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 ·7x
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
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = sin(x – 2) + x2
Using derivative, prove that: tan –1x + cot–1x = `pi/(2)`
Find the marginal demand of a commodity where demand is x and price is y.
y = `(5"x" + 9)/(2"x" - 10)`
State whether the following is True or False:
If f′ is the derivative of f, then the derivative of the inverse of f is the inverse of f′.
If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.
Differentiate `tan^-1[(sqrt(1 + x^2) - 1)/x]` w.r. to `tan^-1[(2x sqrt(1 - x^2))/(1 - 2x^2)]`
The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = xe–x + 7
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 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
The I.F. of differential equation `dy/dx+y/x=x^2-3 "is" log x.`
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`
