What is the derivative of X^(x^x)?

  • Thread starter Thread starter appplejack
  • Start date Start date
  • Tags Tags
    Derivative
appplejack
Messages
43
Reaction score
0

Homework Statement


I uploaded a image file of the question.


Homework Equations


I've seen the derivative of X^x but how do I do this one?


The Attempt at a Solution

 

Attachments

  • 1111.jpg
    1111.jpg
    1.4 KB · Views: 357
Physics news on Phys.org
Put t=xx and apply the chain rule since you know what d/dx(xsup]x[/sup]) gives.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

How do I compute the derivative of (x^x)^(x^x)^(x^x)....
Replies
29
Views
2K
Trying To Use Squeeze Theorem To Prove Derivatives Are Equal
Replies
4
Views
1K
If f is undefined at x=a, can f' exist at x=a?
Replies
9
Views
1K
Why Is the Chain Rule Not Used in Differentiating h(x) = 3f(x) + 8g(x)?
Replies
2
Views
2K
Derivative of -x using first principle
Replies
5
Views
2K
Determine for which x the derivative exists of: ##f(x)=\ln|\sin(x)|##
Replies
2
Views
1K
Exam asks me for a case where ▲x > dx?
Replies
5
Views
1K
Determine for which x the derivative exists for $$f(x)=arcsin(\sqrt x)$$
Replies
16
Views
2K
Existence of directional derivative
Replies
4
Views
1K
Find f(x,y) given partial derivative and initial condition
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top