Advertisements
Advertisements
Question
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
Options
1
`1/2`
`1/3`
`1/4`
Solution
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = `bb(1/4)`.
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 = `sqrt(2 - sqrt(x)`
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(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 = e2x-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 ·7x
Find the derivative of the inverse function of the following : y = x2 + log x
Find the derivative of the inverse function of the following : y = x 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: tan –1x + cot–1x = `pi/(2)`
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 rate of change of demand (x) of a commodity with respect to its price (y) if y = 18x + log(x - 4).
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 = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`
If y = `tan^-1((2x)/(1 - x^2))`, x ∈ (−1, 1) then `("d"y)/("d"x)` = ______.
If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______
Let f(x) = x5 + 2x – 3 find (f−1)'(-3)
Find the derivative of cos−1x w.r. to `sqrt(1 - x^2)`
Differentiate `tan^-1[(sqrt(1 + x^2) - 1)/x]` w.r. to `tan^-1[(2x sqrt(1 - x^2))/(1 - 2x^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:
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")` = ?
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
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
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)`
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.
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+25x^2`
