Advertisements
Advertisements
प्रश्न
Find the derivative of the inverse function of the following : y = x2 + log x
उत्तर
y = x2 + log x
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x^2 + logx)`
= `"d"/"dx"(x^2) + "d"/"dx"(logx)`
= `2x + 1/x`
= `(2x^2 + 1)/(x`
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(((2x^2 + 1)/x)`
= `x/(2x^2 + 1)`.
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 = `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 = `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 = 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 = `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 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 = 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
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).
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)`
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"`
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)
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)`
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)`
If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.
I.F. of dx = y (x + y ) dy is a function of ______.
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`
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.
