Home
Class 12
MATHS
The function f(x)=e^x+x , being differen...

The function `f(x)=e^x+x ,` being differentiable and one-to-one, has a differentiable inverse `f^(-1)(x)dot` The value of `d/(dx)(f^(-1))` at the point `f(log2)` is `1/(1n2)` (b) `1/3` (c) `1/4` (d) none of these

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 9|3 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=e^(x)+x, being differentiable and one-to-one,has a differentiable inverse f^(-1)(x) .The value of (d)/(dx)(f^(-1)) at the point f(log2) is (a) (1)/(1n2) (b) (1)/(3)( c) (1)/(4) (d) none of these

The function f(x)=e^(x)+x, being differentiable and one- to -one, has a differentiable inverse f^(-1)(x). The value of (x)/(dx)(f^(-1)at f(log2) is

Knowledge Check

  • Let a continous and differentiable function f(x) is such that f(x) and (d)/(dx)f(x) have opposite signs everywhere. Then,

    A
    `f'(x)` is always increasing
    B
    `f(x)` is always increasing
    C
    `|f(x)|` is non - decreasing
    D
    `|f(x)|` is decreasing

    • Similar Questions

    Explore conceptually related problems

    If f(x)=|x|+|x-1|, write the value of (d)/(dx)f(f(x))

    Let f(x)=x^(5)+2x^(3)+3x+4 then the value of 28(d)/(dx)(f^(-1)) at x=-2 is

    Let f(x) be a differentiable and let c a be a constant.Then cf(x) is also differentiable such that (d)/(dx){cf(x)}=c(d)/(dx)(f(x))

    Let f:R rarr R be a one-one onto differentiable function,such that f(2)=1 and f'(2)=3. The find the value of ((d)/(dx)(f^(-1)(x)))_(x=1)

    If f(x)=x+1, then write the value of (d)/(dx)(fof)(x)

    If adifferentiabl e function f(x)=e^(x)+2x is given,then equal to (d)/(dx)(f^(-1)(x)) at x=f(ln3) is equal to

    If (d)/(dx)(f(x))=4x such that f(2)=0, then f(x) is

    Home
    Profile