Advertisements
Advertisements
प्रश्न
If g is the inverse of f and f'(x) = `1/(1 + x^4)` then g'(x) = ______
पर्याय
`1/(1 + ["g"(x)]^4`
`(4x^3)/(1 + x^4)`
`1/(1 + ["g"(x)]^3`
`1 + ["g"(x)]^4`
उत्तर
`1 + ["g"(x)]^4`
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 function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = ex – 3
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 function y = f(x) using the derivative of the inverse function x = f–1(y) in the following: y = `log_2(x/2)`
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 = 3x2 + 2logx3
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
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 :
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25x + log(1 + x2)
Find the marginal demand of a commodity where demand is x and price is y.
y = `"x"*"e"^-"x" + 7`
Find the marginal demand of a commodity where demand is x and price is y.
y = `("x + 2")/("x"^2 + 1)`
Find the marginal demand of a commodity where demand is x and price is y.
y = `(5"x" + 9)/(2"x" - 10)`
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 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
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)`
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 `dy/dx`, if y = `sec^-1((1 + x^2)/(1 - x^2))`.
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
