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

`(1)/(1n2)`

`(1)/(3)`

`(1)/(4)`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DIFFERENTIATION
ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos
DIFFERENTIATION
ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|16 Videos
DIFFERENTIATION
ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|7 Videos
DIFFERENTIAL EQUATION
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos
DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS
ARIHANT MATHS ENGLISH|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)dot 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

is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not differentiable at (a)-1 (b)0 (c)1 (d)2

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

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))dot

Let f: RvecR be a one-one onto differentiable function, such that f(2)=1a n df^(prime)(2)=3. The find the value of ((d/(dx)(f^(-1)(x))))_(x=1)

Let f: R → R be a one-one onto differentiable function, such that f(2)=1 and f^(prime)(2)=3. Then, 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) .

Differentiate f(x)=tan 2x by first principle of differentiation.

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these

ARIHANT MATHS ENGLISH-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)

If y=(sin^(-1)(sinalphasinx)/(1-cosalphasinx)), then y'(0) is equal to
Text Solution
|
If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals
Text Solution
|
The function f(x)=e^x+x , being differentiable and one-to-one, has a d...
Text Solution
|
If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 a...
Text Solution
|
about to only mathematics
Text Solution
|
If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...
Text Solution
|
If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals
Text Solution
|
Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...
Text Solution
|
if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...
Text Solution
|
If f(x)=cos^(-1)1/(sqrt(13))(2cosx-3sinx) +sin^(-1)1/(sqrt(13))x(2cos...
Text Solution
|
If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...
Text Solution
|
Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...
Text Solution
|
If f(x)=(a+sqrt(a^2-x^2)+x)/(sqrt(a^2-x^2)+a-x) where a>0 then f'(0) ...
Text Solution
|
Let u/x a n dv(x) be differentiable functions such that (u(x))/(v(x))=...
Text Solution
|
If f(x) =|log(e)|x||, then f'(x) equals
Text Solution
|
If f(x) is given by f(x)=(cosx+i sinx)(cos3x+isin3x)......... .......
Text Solution
|
Let f(x)=x^(n) , n being a non-negative integer, The value of n for w...
Text Solution
|
If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...
Text Solution
|
The function u=e^x sin x ; v=e^x cos x satisfy the equation a.v(d u...
Text Solution
|
If f(x)=log(x^(2))(logx),then f '(x)at x= e is
Text Solution
|