Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
y = x5 + 2x3 + 3x
Differentiating w.r.t. x, we get
`"dy"/"dx" ="d"/"dx"(x^5 + 2x^3 + 3x)`
= 5x4 + 2 x 3x2 + 3 x 1
= 5x4 + 6x2 + 3
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(5x^4 + 6x^2 + 3)`
At x = `1, "dx"/"dy"`
= `(1)/(5x^4 + 6x^2 + 3)_(at x = 1)`
= `(1)/(5(1)^4 + 6(1)^2 + 3)`
= `(1)/(5 + 6 + 3)`
= `(1)/(14)`.
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 = log(2x – 1)
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 = x2·ex
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 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 = ex + 3x + 2
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
If f(x) = x3 + x − 2, find (f−1)'(0).
Using derivative, prove that: sec–1x + cosec–1x = `pi/(2)` ...[for |x| ≥ 1]
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 :
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 marginal demand of a commodity where demand is x and price is y.
y = `"x"*"e"^-"x" + 7`
If y = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`
If `"x"^3 + "y"^2 + "xy" = 7` Find `"dy"/"dx"`
If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.
Find the derivative of the inverse of function y = 2x3 – 6x and calculate its value at x = −2
Let f(x) = x5 + 2x – 3 find (f−1)'(-3)
Find the derivative of cos−1x w.r. to `sqrt(1 - x^2)`
Choose the correct alternative:
What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x3.
Choose the correct alternative:
If x = at2, y = 2at, then `("d"^2y)/("d"x^2)` = ?
The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = 5 + x2e–x + 2x
State whether the following statement is True or False:
If y = 10x + 1, then `("d"y)/("d"x)` = 10x.log10
State whether the following statement is True or False:
If y = 7x + 1, then the rate of change of demand (x) of a commodity with respect to its price (y) is 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 the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x2e–x + 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)`
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
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 + 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 + 25x2
