Advertisements
Advertisements
Question
If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______
Options
`1/(1 + ["g"(x)]^4`
`(4x^3)/(1 + x^4)`
`1/(1 + ["g"(x)]^3`
`1 + ["g"(x)]^4`
Solution
`1 + ["g"(x)]^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 = 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 = 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 = 3x2 + 2logx3
If f(x) = x3 + x – 2, find (f–1)'(0).
Using derivative, prove that: tan –1x + cot–1x = `pi/(2)`
Using derivative, prove that: sec–1x + cosec–1x = `pi/(2)` ...[for |x| ≥ 1]
Find the marginal demand of a commodity where demand is x and price is y.
y = `"x"*"e"^-"x" + 7`
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 `"x"^3 + "y"^2 + "xy" = 7` Find `"dy"/"dx"`
If `"x"^3"y"^3 = "x"^2 - "y"^2`, Find `"dy"/"dx"`
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)]`
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 xm. yn = `("x" + "y")^(("m" + "n"))`, then `("dy")/("dx")` = ?
Choose the correct alternative:
If x = at2, y = 2at, then `("d"^2y)/("d"x^2)` = ?
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x2e–x + 2x
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
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 + 25x2
Find the rate of change of demand (x) of a commodity with respect to its price (y) if `y=12+10x+25x^2`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x2.
