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x^(1/x)
The derivative of the function/ 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
x1⋅1xx^{1 \cdot \frac{1}{x}} 
d /x ___\
--\\/ x /
dx
ddxx1⋅1x\frac{d}{d x} x^{1 \cdot \frac{1}{x}}
Transform
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

    (1⋅1x)1x(log⁡(1⋅1x)+1)\left(1 \cdot \frac{1}{x}\right)^{\frac{1}{x}} \left(\log{\left(1 \cdot \frac{1}{x} \right)} + 1\right)

  2. Now simplify:

    (log⁡(1x)+1)(1x)1x\left(\log{\left(\frac{1}{x} \right)} + 1\right) \left(\frac{1}{x}\right)^{\frac{1}{x}}

The answer is:

(log⁡(1x)+1)(1x)1x\left(\log{\left(\frac{1}{x} \right)} + 1\right) \left(\frac{1}{x}\right)^{\frac{1}{x}}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
x ___ /1    log(x)\
\/ x *|-- - ------|
      | 2      2  |
      \x      x   /
x1x(−log⁡(x)x2+1x2)x^{\frac{1}{x}} \left(- \frac{\log{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}\right)
Simplify
The second derivative [src] 
      /                             2\
x ___ |                (-1 + log(x)) |
\/ x *|-3 + 2*log(x) + --------------|
      \                      x       /
--------------------------------------
                   3                  
                  x
x1x(2log⁡(x)−3+(log⁡(x)−1)2x)x3\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}}
Simplify
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
−x1x(6log⁡(x)−11+3(log⁡(x)−1)(2log⁡(x)−3)x+(log⁡(x)−1)3x2)x4- \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}}
Simplify
The graph
Derivative of x^(1/x)
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