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x^(1/x)

Derivative of x^(1/x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
x ___
\/ x 
$$x^{1 \cdot \frac{1}{x}}$$
d /x ___\
--\\/ x /
dx       
$$\frac{d}{d x} x^{1 \cdot \frac{1}{x}}$$
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
x ___ /1    log(x)\
\/ x *|-- - ------|
      | 2      2  |
      \x      x   /
$$x^{\frac{1}{x}} \left(- \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}\right)$$
The second derivative [src]
      /                             2\
x ___ |                (-1 + log(x)) |
\/ x *|-3 + 2*log(x) + --------------|
      \                      x       /
--------------------------------------
                   3                  
                  x                   
$$\frac{x^{\frac{1}{x}} \left(2 \log{\left(x \right)} - 3 + \frac{\left(\log{\left(x \right)} - 1\right)^{2}}{x}\right)}{x^{3}}$$
The third derivative [src]
       /                              3                                  \ 
 x ___ |                 (-1 + log(x))    3*(-1 + log(x))*(-3 + 2*log(x))| 
-\/ x *|-11 + 6*log(x) + -------------- + -------------------------------| 
       |                        2                        x               | 
       \                       x                                         / 
---------------------------------------------------------------------------
                                      4                                    
                                     x                                     
$$- \frac{x^{\frac{1}{x}} \left(6 \log{\left(x \right)} - 11 + \frac{3 \left(\log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} - 3\right)}{x} + \frac{\left(\log{\left(x \right)} - 1\right)^{3}}{x^{2}}\right)}{x^{4}}$$
The graph
Derivative of x^(1/x)