If y=e^(x^(e^x)), find dy/dx....

If `y=e^(x^(e^x))`, find `dy/dx`.

Text Solution

Verified by Experts

The correct Answer is:

`(dy)/(dx)=(y^(2)logy)/(x(1-ylogylogx))`

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
ARIHANT PRAKASHAN|Exercise Topic 2 (practice question (6 mark question)|8 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT PRAKASHAN|Exercise Topic 2 (Topic test 2)|9 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT PRAKASHAN|Exercise Topic 2 (practice question (1 mark question)|15 Videos
CHSE ODISHA EXAMINATION PAPER 2020
ARIHANT PRAKASHAN|Exercise GROUP C (30 MARKS) 11. ANSWER ANY ONE QUESTIONS |2 Videos
DETERMINANTS
ARIHANT PRAKASHAN|Exercise CHAPTER TEST (6 MARK QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

If y=e^(x^(e^(x^(e^x)))) , then find dy/dx .

If e^x+e^y=e^(x+y) , find dy/dx .

If y=x^4e^(2x) ,then find, dy/dx .

If e^(x)+e^(y) = e(x+y) find dy/dx .

If y=e^x+a^x+x^x , then find dy/dx at x=a

if y=e^(cos^(-1)x) then find dy/dx .

If x^(y) = e^(x-y) then find dy/dx .

If y = 5^t and t=e^3x , find dy/dx at x=0 .

If y^(x)=x^(y) , then find (dy)/(dx) .

If y = x+e^(x) ,then find d^(2)x/dy^(2) .

ARIHANT PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Topic 2 (practice question (4 mark question)

If y=e^(x^(e^x)), find dy/dx.
03:16
|
Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...
11:35
|
Differentiate y=(siny)^(sin2x)
07:09
|
Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))
05:29
|
Find dy/dx if x^m y^n = (x/y)^(m+n)
02:23
|
Find (dy)/(dx), when y^(x)=x^(siny)
04:12
|
Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)
05:31
|
If y=cosec^(-1)x, then find (dy)/(dx) and determine its value at x=-2.
01:44
|
Examine the differentiability to log|x| for all real values of x.
04:16
|
Find the derivative of x^(sinx) w.r.t.x.
03:28
|
Differentiate. sin^(-1)((2x)/(1+x^2))w.r.t.cos^(-1)((1-x^2)/(1+x^2))
04:33
|
If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a
05:02
|
Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx
04:44
|
Differentiate y=2^(x^(2))+tan^(-1)((cosx-sinx)/(cos x+sinx)) w.r.t. x.
04:47
|
Write, why the function sin^(-1)((1)/(sqrt(1-x^(2)))) cannot be differ...
Text Solution
|
Prove that y=tan(x+y), then (dy)/(dx)=(1+y^(2))/(-y^(2))
04:34
|
Find the derivative of tan^(-1)(1+x^(2)) with respect to log(x^(2)+1)
03:43
|
If y=sin^(-1)((2sqrt(x^(2)-1))/(x^(2))) , then find (dy)/(dx).
04:03
|
Find dy/dx, sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2)
04:29
|
If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y.
02:57
|